History of quantum mechanics

<h2 id="triumph-and-trouble-at-the-end-of-the-classical-era">Triumph and trouble at the end of the classical era</h2>
The <a href="/facts/History_of_physics/aXKxL48L">discoveries of the 19th century</a>, both the successes and failures, set the stage for the emergence of quantum mechanics.

<h3>Wave theory of light</h3>
Beginning in 1670 and progressing over three decades, <a href="/facts/Isaac_Newton/4L7gTncN">Isaac Newton</a> developed and championed his <a href="/facts/Corpuscular_theory/8bq1oJym">corpuscular theory</a>, arguing that the perfectly straight lines of reflection demonstrated light's particle nature, as at that time no wave theory demonstrated travel in straight lines.<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a>: 19  He explained refraction by positing that particles of light accelerated laterally upon entering a denser medium. Around the same time, Newton's contemporaries <a href="/facts/Robert_Hooke/T5sEElp5">Robert Hooke</a> and <a href="/facts/Christiaan_Huygens/GtBqoBVm">Christiaan Huygens</a>, and later <a href="/facts/Augustin-Jean_Fresnel/jb64tyGc">Augustin-Jean Fresnel</a>, mathematically refined the wave viewpoint, showing that if light traveled at different speeds in different media, refraction could be easily explained as the medium-dependent propagation of light waves. The resulting <a href="/facts/Huygens%25E2%2580%2593Fresnel_principle/t7lsjjA3">Huygens–Fresnel principle</a> was extremely successful at reproducing light's behaviour and was consistent with <a href="/facts/Thomas_Young_(scientist)/X4RtR47L">Thomas Young</a>'s discovery of <a href="/facts/Wave_interference/lI5f78I4">wave interference</a> of light by his <a href="/facts/Double-slit_experiment/TR8zwEcy">double-slit experiment</a> in 1801.<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a> The wave view did not immediately displace the ray and particle view, but began to dominate scientific thinking about light in the mid 19th century, since it could explain polarization phenomena that the alternatives could not.<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a>
<a href="/facts/James_Clerk_Maxwell/jtYyze61">James Clerk Maxwell</a> found that he could apply his previously discovered <a href="/facts/Maxwell%2527s_equations/LfJ1drHS"> equations</a>, along with a slight modification, to describe self-propagating waves of oscillating electric and magnetic fields. It quickly became apparent that visible light, ultraviolet light, and infrared light were all electromagnetic waves of differing frequency.<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a>: 272  This theory became a critical ingredient in the beginning of quantum mechanics.

<h3>Emerging atomic theory</h3>
During the early 19th century, <a href="/facts/Chemistry/SrNqkGVm">chemical</a> research by <a href="/facts/John_Dalton/oS8grQR4">John Dalton</a> and <a href="/facts/Amedeo_Avogadro/qG6Rq5Wc">Amedeo Avogadro</a> lent weight to the <a href="/facts/Atomic_theory/B2WvuLf6">atomic theory</a> of matter, an idea that <a href="/facts/James_Clerk_Maxwell/jtYyze61">James Clerk Maxwell</a>, <a href="/facts/Ludwig_Boltzmann/xDeLroqt">Ludwig Boltzmann</a> and others built upon to establish the <a href="/facts/Kinetic_theory_of_gases/WUaJuMHU">kinetic theory of gases</a>. The successes of kinetic theory gave further credence to the idea that matter is composed of atoms, yet the theory also had shortcomings that would only be resolved by the development of quantum mechanics.<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> The existence of atoms was not universally accepted among physicists or chemists; <a href="/facts/Ernst_Mach/gfSFynYK">Ernst Mach</a>, for example, was a staunch anti-atomist.<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a>

The earliest hints of problems in classical mechanics were raised in relation to the temperature dependence of the properties of gasses.<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a>
<a href="/facts/Ludwig_Boltzmann/xDeLroqt">Ludwig Boltzmann</a> suggested in 1877 that the energy levels of a physical system, such as a <a href="/facts/Molecule/N9ljSfFq">molecule</a>, could be discrete (rather than continuous). Boltzmann's rationale for the presence of discrete energy levels in molecules such as those of iodine gas had its origins in his <a href="/facts/Statistical_thermodynamics/6zMsNYYG">statistical thermodynamics</a> and <a href="/facts/Statistical_mechanics/6zMsNYYG">statistical mechanics</a> theories and was backed up by <a href="/facts/Mathematical/pxTouaz4">mathematical</a> arguments, as would also be the case twenty years later with the first <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum theory</a> put forward by <a href="/facts/Max_Planck/KKk0698y">Max Planck</a>.

<h3>Electrons and the nucleus</h3>
In the final days of the 1800s, <a href="/facts/J._J._Thomson/Y4jyndJF">J. J. Thomson</a> established that <a href="/facts/Electron/L0KBo5cW">electrons</a> carry a negative charge opposite but the same size as that of a hydrogen ion while having a mass over one thousand times less. Many such electrons were known to be associated with every atom.<a class="footnote-ref" id="fnref:12" href="#fn:12">12</a>: 365  By 1904 Thomson proposed the first atomic model with subatomic constituents, using circulating electrons in a background of positive charge, the so-called <a href="/facts/Plum_pudding_model/Bw7K1yXo">plum pudding model</a>.<a class="footnote-ref" id="fnref:13" href="#fn:13">13</a> Thomson's concepts were supported by early <a href="/facts/Beta_particle/x8b3ttLn">beta particle</a> scattering experiments but by 1911 <a href="/facts/Hans_Geiger/SGNJNM2g">Hans Geiger</a> and his student <a href="/facts/Ernest_Marsden/tW2u740z">Ernest Marsden</a> demonstrated <a href="/facts/Rutherford_scattering_experiments/cmgI1Ha9">backscattering of alpha particles</a> which <a href="/facts/Ernest_Rutherford/hjjMEskl">Ernest Rutherford</a> interpreted as compelling evidence that the positive charge was concentrated in a small volume we now call the <a href="/facts/Atomic_nucleus/orpIm5Xl">nucleus</a>.<a class="footnote-ref" id="fnref:14" href="#fn:14">14</a>

<h3>Radiation theory</h3>

Throughout the 1800s many studies investigated details in the <a href="/facts/Spectral_line/HuI4Bj5f">spectrum</a> of intensity versus frequency for light emitted by flames, by the Sun, or red-hot objects.<a class="footnote-ref" id="fnref:15" href="#fn:15">15</a>: 367  The <a href="/facts/Rydberg_formula/xKRGYj5V">Rydberg formula</a> effectively summarized the dark lines seen in the spectrum, but Rydberg provided no physical model to explain them. The spectrum emitted by red-hot objects could be explained at high or low wavelengths but the two theories differed.

<h2 id="old-quantum-theory">Old quantum theory</h2>
Quantum mechanics developed in two distinct phases. The first phase, known as the <a href="/facts/Old_quantum_theory/pXkHwvrh">old quantum theory</a>, began around 1900 with radically new approaches to explanations physical phenomena not understood by classical mechanics of the 1800s.<a class="footnote-ref" id="fnref:16" href="#fn:16">16</a>

<h3>Planck introduces quanta to explain black-body radiation</h3>
Main article: <a href="/facts/Ultraviolet_catastrophe/rRM4PTQU">Ultraviolet catastrophe</a>

<a href="/facts/Thermal_radiation/1PD9jtCv">Thermal radiation</a> is electromagnetic radiation emitted from the surface of an object due to the object's internal energy. If an object is heated sufficiently, it starts to emit light at the red end of the visible <a href="/facts/Spectrum/wPUjkpqI">spectrum</a>, as it becomes red hot.
Heating it further causes the color to change from red to yellow, white, and blue, as it emits light at increasingly shorter wavelengths (higher frequencies). A perfect emitter is also a perfect absorber: when it is cold, such an object looks perfectly black, because it absorbs all the light that falls on it and emits none. Consequently, an ideal thermal emitter is known as a <a href="/facts/Black_body/f0fHghDy">black body</a>, and the radiation it emits is called <a href="/facts/Black-body_radiation/f0fHghDy">black-body radiation</a>.

By the late 19th century, thermal radiation had been fairly well characterized experimentally. Several formulas had been created that could describe some of the experimental measurements of thermal radiation: how the wavelength at which the radiation is strongest changes with temperature is given by <a href="/facts/Wien%2527s_displacement_law/nrMVYWTF">Wien's displacement law</a>, the overall power emitted per unit area is given by the <a href="/facts/Stefan%25E2%2580%2593Boltzmann_law/vA4tbwKC">Stefan–Boltzmann law</a>. The best theoretical explanation of the experimental results was the <a href="/facts/Rayleigh%25E2%2580%2593Jeans_law/qlvgQ5jb">Rayleigh–Jeans law</a>, which agrees with experimental results well at large wavelengths (or, equivalently, low frequencies), but strongly disagrees at short wavelengths (or high frequencies). In fact, at short wavelengths, classical physics predicted that energy will be emitted by a hot body at an infinite rate. This result, which is clearly wrong, is known as the <a href="/facts/Ultraviolet_catastrophe/rRM4PTQU">ultraviolet catastrophe</a>. However, classical physics led to the Rayleigh–Jeans law, which, as shown in the figure, agrees with experimental results well at low frequencies, but strongly disagrees at high frequencies. Physicists searched for a single theory that explained all the experimental results.

The first model that was able to explain the full spectrum of thermal radiation was put forward by <a href="/facts/Max_Planck/KKk0698y">Max Planck</a> in 1900.<a class="footnote-ref" id="fnref:17" href="#fn:17">17</a> He proposed a mathematical model in which the thermal radiation was in equilibrium with a set of <a href="/facts/Harmonic_oscillator/7IQNToGt">harmonic oscillators</a>. To reproduce the experimental results, he had to assume that each oscillator emitted an integer number of units of energy at its single characteristic frequency, rather than being able to emit any arbitrary amount of energy. In other words, the energy emitted by an oscillator was quantized. According to Planck, the quantum of energy E of a light quantum is proportional to its frequency <a href="/facts/Frequency/QUSbPaW8">frequency</a> ν. As an equation is it written:

E
        =
        h
        v
        .
      
    
    {\displaystyle E=hv.}

This is now known as the <a href="/facts/Planck_relation/KR8u3qPV">Planck relation</a> and the proportionality constant, h, as the <a href="/facts/Planck_constant/qGHAe3qq">Planck constant</a>.
Planck's law was the first quantum theory in physics, and Planck won the 1918 <a href="/facts/Nobel_Prize_in_Physics/o6w1nCbr">Nobel Prize in Physics</a> "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".<a class="footnote-ref" id="fnref:18" href="#fn:18">18</a> At the time, however, Planck's view was that quantization was purely a <a href="/facts/Heuristic/BcBEkv9c">heuristic</a> mathematical construct, rather than (as is now believed) a fundamental change in our understanding of the world.<a class="footnote-ref" id="fnref:19" href="#fn:19">19</a>

<h3>Einstein applies quanta to explain the photoelectric effect</h3>
Main article: <a href="/facts/Photoelectric_effect/gIDcdm5U">Photoelectric effect</a>

In 1887, <a href="/facts/Heinrich_Hertz/sbL2MSpM">Heinrich Hertz</a> observed that when light with sufficient frequency hits a metallic surface, the surface emits <a href="/facts/Cathode_rays/9jRXSquS">cathode rays</a>.<a class="footnote-ref" id="fnref:20" href="#fn:20">20</a>: I:362  Ten years later, J. J. Thomson showed that the many reports of cathode rays were actually "corpuscles" and they quickly came to be called <a href="/facts/Electrons/L0KBo5cW">electrons</a>. In 1902, <a href="/facts/Philipp_Lenard/e2MYF17W">Philipp Lenard</a> discovered that the maximum possible energy of an ejected electron is unrelated to the <a href="/facts/Intensity_(physics)/KFWkJkJI">intensity</a> of the monochromatic light.<a class="footnote-ref" id="fnref:21" href="#fn:21">21</a> This observation is at odds with classical electromagnetism, which predicts that the electron's energy should be proportional to the intensity of the incident radiation.<a class="footnote-ref" id="fnref:22" href="#fn:22">22</a>: 24

In 1905, <a href="/facts/Albert_Einstein/CNTet8qu">Albert Einstein</a> suggested that even though continuous models of light worked extremely well for time-averaged optical phenomena, for instantaneous transitions the energy in light may occur a finite number of energy quanta. 
In the introduction section of his March 1905 paper "On a Heuristic Viewpoint Concerning the Emission and Transformation of Light", Einstein states:

<blockquote>According to the assumption to be contemplated here, when a light ray is spreading from a point, the energy is not distributed continuously over ever-increasing spaces, but consists of a finite number of "energy quanta" that are localized in points in space, move without dividing, and can be absorbed or generated only as a whole.<a class="footnote-ref" id="fnref:23" href="#fn:23">23</a></blockquote>
This has been called the most "revolutionary" sentence written by a twentieth century physicist, meaning that it proposed an idea altered mainstream thinking.<a class="footnote-ref" id="fnref:24" href="#fn:24">24</a>: 143  
<a href="/facts/Photon_energy/Gy4zEAaE">The energy of a single quantum</a> of light of frequency 
 
 
 
 f
 
 
 {\displaystyle f}
 
 is given by the frequency multiplied by the Planck constant 
 
 
 
 h
 
 
 {\displaystyle h}
 
:

E
        =
        h
        f
      
    
    {\displaystyle E=hf}

Einstein assumed a light quanta transfers all of its energy to a single electron imparting at most an energy hf to the electron. Therefore, only the light frequency determines the maximum energy that can be imparted to the electron; the intensity of the photoemission is proportional to the light beam intensity.<a class="footnote-ref" id="fnref:25" href="#fn:25">25</a>
Einstein argued that it takes a certain amount of energy, called the <a href="/facts/Work_function/VHaHTyXg">work function</a> and denoted by φ, to remove an electron from the metal.<a class="footnote-ref" id="fnref:26" href="#fn:26">26</a> This amount of energy is different for each metal. If the energy of the light quanta is less than the work function, then it does not carry sufficient energy to remove the electron from the metal. The threshold frequency, f0, is the frequency of a light quanta whose energy is equal to the work function:

φ
        =
        h
        
          f
          
            0
          
        
        .
      
    
    {\displaystyle \varphi =hf_{0}.}

If f is greater than f0, the energy hf is enough to remove an electron. The ejected electron has a <a href="/facts/Kinetic_energy/aJRxUd4p">kinetic energy</a>, Ek, which is, at most, equal to the light energy minus the energy needed to dislodge the electron from the metal:

E
          
            k
          
        
        =
        h
        f
        −
        φ
        =
        h
        (
        f
        −
        
          f
          
            0
          
        
        )
        .
      
    
    {\displaystyle E_{\text{k}}=hf-\varphi =h(f-f_{0}).}

Einstein's description of light as being composed of energy quanta extended Planck's notion of quantized energy, which is that a single quantum of a given frequency, f, delivers an invariant amount of energy, hf. Einstein was awarded the 1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect".<a class="footnote-ref" id="fnref:27" href="#fn:27">27</a> 
In nature, single quanta are rarely encountered. The Sun and emission sources available in the 19th century emit a vast amount of energy every second. The <a href="/facts/Planck_constant/qGHAe3qq">Planck constant</a>, h, is so tiny that the amount of energy in each quantum, hf is very very small. Light we see includes many trillions of such quanta. <a href="/facts/Arthur_Compton/FrNYLBj4">Arthur Compton</a>'s demonstration of the <a href="/facts/Compton_scattering/Q98Ty8rz"> scattering</a> of light by electrons scattering convinced physicists of the reality of photons.<a class="footnote-ref" id="fnref:28" href="#fn:28">28</a> Compton won the 1927 Nobel Prize in Physics for his discovery.<a class="footnote-ref" id="fnref:29" href="#fn:29">29</a> The term "<a href="/facts/Photon/mFNhAEzA">photon</a>" was introduced in 1926 by <a href="/facts/Gilbert_N._Lewis/wWnV6QXL">Gilbert N. Lewis</a>.<a class="footnote-ref" id="fnref:30" href="#fn:30">30</a>

<h3>Quantization of matter: the Bohr model of the atom</h3>
Main article: <a href="/facts/Bohr_model/FmTHjaxy">Bohr model</a>
<a href="/facts/Ernest_Rutherford/hjjMEskl">Ernest Rutherford</a>'s discovery of the atomic nucleus in 1911 did not immediately cause atomic models to be revised. Mechanical models with circulating electrons had been proposed for many years but they were known to be unstable.<a class="footnote-ref" id="fnref:31" href="#fn:31">31</a>
A second, related puzzle was the <a href="/facts/Emission_spectrum/fxumR717">emission spectrum</a> of atoms. When a gas is heated, it gives off light only at discrete frequencies. For example, the visible light given off by <a href="/facts/Hydrogen/BoYHjl0J">hydrogen</a> consists of four different colors, as shown in the picture below. The intensity of the light at different frequencies is also different. By contrast, white light consists of a continuous emission across the whole range of visible frequencies. By the end of the nineteenth century, a simple rule known as <a href="/facts/Balmer_series/Vc4s4SIt">Balmer's formula</a> showed how the frequencies of the different lines related to each other, though without explaining why this was, or making any prediction about the intensities. The formula also predicted some additional spectral lines in ultraviolet and infrared light that had not been observed at the time. These lines were later observed experimentally, raising confidence in the value of the formula.

<a href="/facts/Emission_spectrum/fxumR717">Emission spectrum</a> of <a href="/facts/Hydrogen/BoYHjl0J">hydrogen</a>. When excited, hydrogen gas gives off light in four distinct colors (spectral lines) in the visible spectrum, as well as a number of lines in the infrared and ultraviolet.

In 1913, H. M. Hansen asked <a href="/facts/Niels_Bohr/ydLPvQXT">Niels Bohr</a> about Balmer's formula. Bohr recalled that "As soon as I saw Balmer's formula, the whole thing was immediately clear to me."<a class="footnote-ref" id="fnref:32" href="#fn:32">32</a> In "On the Constitution of Atoms and Molecules", he proposed <a href="/facts/Bohr_model/FmTHjaxy"> a new model of the atom</a> that included quantized electron orbits. In the Bohr model, the hydrogen atom is pictured as a heavy, positively charged nucleus orbited by a light, negatively charged electron. The electron can only exist in certain, discretely separated orbits, labeled by their <a href="/facts/Angular_momentum/7TuSVFxq">angular momentum</a>, which is restricted to be an integer multiple of the <a href="/facts/Reduced_Planck_constant/qGHAe3qq">reduced Planck constant</a>.<a class="footnote-ref" id="fnref:33" href="#fn:33">33</a> The electron moves to a higher or lower orbital by absorbing or emitting a photon of corresponding frequency. 
These orbits had fixed or quantized values of angular momentum, a concept proposed by <a href="/facts/John_William_Nicholson/5NYm5VAK">John William Nicholson</a> in a nuclear atom model and adopted by Bohr in his model.<a class="footnote-ref" id="fnref:34" href="#fn:34">34</a>: 169  When an atom emitted (or absorbed) energy, the electron did not move in a continuous trajectory from one orbit around the nucleus to another, as might be expected classically. Instead, the electron would jump instantaneously from one orbit to another, giving off the emitted light in the form of a photon.<a class="footnote-ref" id="fnref:35" href="#fn:35">35</a> The possible energies of photons given off by each element were determined by the differences in energy between the orbits, and so the emission spectrum for each element would contain a number of lines.<a class="footnote-ref" id="fnref:36" href="#fn:36">36</a>
The model's key success lay in explaining the Rydberg formula for the spectral <a href="/facts/Hydrogen_spectral_series/BhTeHzBt">emission lines</a> of atomic hydrogen by using the transitions of electrons between orbits.<a class="footnote-ref" id="fnref:37" href="#fn:37">37</a>: 276  While the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. Not only did the Bohr model explain the reasons for the structure of the Rydberg formula, it also provided a justification for the fundamental physical constants that make up the formula's empirical results.

Starting from only one simple assumption about the rule that the orbits must obey, the Bohr model was able to relate the observed spectral lines in the emission spectrum of hydrogen to previously known constants. In Bohr's model, the electron was not allowed to emit energy continuously and crash into the nucleus: once it was in the closest permitted orbit, it was stable forever. Bohr's model did not explain why the orbits should be quantized in that way, nor was it able to make accurate predictions for atoms with more than one electron, or to explain why some spectral lines are brighter than others.
Some fundamental assumptions of the Bohr model were soon proven wrong—but the key result that the discrete lines in emission spectra are due to some property of the electrons in atoms being quantized is correct. The way that the electrons actually behave is strikingly different from Bohr's atom, and from what we see in the world of our everyday experience; this modern quantum mechanical model of the atom is discussed below.

Moreover, the application of Planck's quantum theory to the electron allowed <a href="/facts/%25C8%2598tefan_Procopiu/6vbNz2bW">Ștefan Procopiu</a> in 1911–1913, and subsequently Niels Bohr in 1913, to calculate the <a href="/facts/Magnetic_moment/VpAQKJtr">magnetic moment</a> of the <a href="/facts/Electron/L0KBo5cW">electron</a>, which was later called the "<a href="/facts/Bohr_magneton/sK2YxXAk">magneton</a>"; similar quantum computations, but with numerically quite different values, were subsequently made possible for both the magnetic moments of the <a href="/facts/Proton/clCjepXP">proton</a> and the <a href="/facts/Neutron/oRCM1geb">neutron</a> that are three <a href="/facts/Order_of_magnitude/cWzRP2dM">orders of magnitude</a> smaller than that of the electron.
These theories, though successful, were strictly <a href="/facts/Phenomenological_model/z8vypElI">phenomenological</a>: during this time, there was no rigorous justification for <a href="/facts/Quantization_(physics)/fvs2Jwpn">quantization</a>, aside, perhaps, from <a href="/facts/Henri_Poincar%25C3%25A9/AazL2j4X">Henri Poincaré</a>'s discussion of Planck's theory in his 1912 paper Sur la théorie des quanta.<a class="footnote-ref" id="fnref:38" href="#fn:38">38</a><a class="footnote-ref" id="fnref:39" href="#fn:39">39</a> They are collectively known as the <a href="/facts/Old_quantum_theory/pXkHwvrh">old quantum theory</a>. Bohr was awarded the 1922 Nobel Prize in Physics "for his services in the investigation of the structure of atoms and of the radiation emanating from them".<a class="footnote-ref" id="fnref:40" href="#fn:40">40</a>

<h3>Spin quantization</h3>
Main article: <a href="/facts/Spin_(physics)/4Jvp7e8P">Spin (physics)</a>
See also: <a href="/facts/Stern%25E2%2580%2593Gerlach_experiment/PCWPE56v">Stern–Gerlach experiment</a>

Quantization of the orbital angular momentum of the electron combined with the magnetic moment of the electron suggested that atoms with a magnetic moment should show quantized behavior in a magnetic field. 
In 1922, <a href="/facts/Otto_Stern/9eP2K5rB">Otto Stern</a> and <a href="/facts/Walther_Gerlach/qEjsbn0c">Walther Gerlach</a> set out to test this theory. They heated silver in a vacuum tube equipped with a series of narrow aligned slits, creating a molecular beam of silver atoms. They shot this beam through an <a href="/facts/Homogeneity_and_heterogeneity/y84KQJxl">inhomogeneous</a> <a href="/facts/Magnetic_field/Ta8Ev588">magnetic field</a>. Rather than a continuous pattern of silver atoms, they found two bunches.<a class="footnote-ref" id="fnref:41" href="#fn:41">41</a>
Relative to its northern pole, pointing up, down, or somewhere in between, in classical mechanics, a magnet thrown through a magnetic field may be deflected a small or large distance upwards or downwards. The atoms that Stern and Gerlach shot through the magnetic field acted similarly. However, while the magnets could be deflected variable distances, the atoms would always be deflected a constant distance either up or down. This implied that the property of the atom that corresponds to the magnet's orientation must be quantized, taking one of two values (either up or down), as opposed to being chosen freely from any angle.
The choice of the orientation of the magnetic field used in the Stern–Gerlach experiment is arbitrary. In the animation shown here, the field is vertical and so the atoms are deflected either up or down. If the magnet is rotated a quarter turn, the atoms are deflected either left or right. Using a vertical field shows that the spin along the vertical axis is quantized, and using a horizontal field shows that the spin along the horizontal axis is quantized.
The results of the Stern-Gerlach experiment caused a sensation, most especially because leading scientists, including Einstein and <a href="/facts/Paul_Ehrenfest/Q3Q7hXeJ">Paul Ehrenfest</a> argued that the silver atoms should have random orientations in the conditions of the experiment: quantization should not have been observable.<a class="footnote-ref" id="fnref:42" href="#fn:42">42</a> At least five years would elapse before this mystery was resolved: quantization was observed but it was not due to orbital angular momentum. Per <a href="/facts/Wolfgang_Pauli/Ugk4ubXk">Wolfgang Pauli</a>'s <a href="/facts/Pauli_exclusion_principle/lsBKGeHD">exclusion principle</a>, only two electrons can occupy the same quantum state at the same time, and their spins must be opposite. Pauli received the 1945 Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or Pauli principle".<a class="footnote-ref" id="fnref:43" href="#fn:43">43</a>
In 1925, <a href="/facts/Ralph_Kronig/e90Wt6F5">Ralph Kronig</a> proposed that electrons behave as if they self-rotate, or "spin", about an axis.<a class="footnote-ref" id="fnref:44" href="#fn:44">44</a>: 56  Spin would generate a tiny magnetic moment that would split the energy levels responsible for spectral lines, in agreement with existing measurements. Two electrons in the same orbital would occupy distinct <a href="/facts/Quantum_state/7jbxd7Dx">quantum states</a> if they "spun" in opposite directions thus satisfying the exclusion principle. Unfortunately, the theory had two significant flaws: two values computed by Kronig were off by a factor of two. Kronig's senior colleagues discouraged his work and it was never published.
Ten months later, Dutch physicists <a href="/facts/George_Uhlenbeck/IVKgKcVF">George Uhlenbeck</a> and <a href="/facts/Samuel_Goudsmit/C5UszfUx">Samuel Goudsmit</a> at <a href="/facts/Leiden_University/MqnmnTtF">Leiden University</a> published their theory of electron self rotation.<a class="footnote-ref" id="fnref:45" href="#fn:45">45</a> The model, like Kronig's was essentially classical but resulted in a quantum prediction.

<h3>de Broglie's matter wave hypothesis</h3>

In 1924, <a href="/facts/Louis_de_Broglie/v696wFwH">Louis de Broglie</a> published a breakthrough hypothesis: <a href="/facts/Matter_waves/Rpszb8f1">matter has wave properties</a>. Building on Einstein's proposal that the photoelectric effect can be described using quantized energy transfers and by Einstein's separate proposal, from special relativity, that mass at rest is equivalent to energy via 
 
 
 
 E
 =
 
 m
 
 0
 
 
 
 c
 
 2
 
 
 
 
 {\displaystyle E=m_{0}c^{2}}
 
, de Broglie proposed that matter in motion appears to have an associated wave with wavelength 
 
 
 
 λ
 =
 h
 
 /
 
 p
 
 
 {\displaystyle \lambda =h/p}
 
 where 
 
 
 
 p
 
 
 {\displaystyle p}
 
 is the matter momentum from the motion.<a class="footnote-ref" id="fnref:46" href="#fn:46">46</a><a class="footnote-ref" id="fnref:47" href="#fn:47">47</a> Requiring his wavelength to encircle an atom, he explained quantization of Bohr's orbits.<a class="footnote-ref" id="fnref:48" href="#fn:48">48</a>: 217  Simultaneously this showed that the wave behavior of light was essentially a quantum effect.<a class="footnote-ref" id="fnref:49" href="#fn:49">49</a>: 216 
De Broglie expanded Bohr's model of the atom by showing that an electron in orbit around a nucleus could be thought of as having wave-like properties. In particular, an electron is observed only in situations that permit a <a href="/facts/Standing_wave/n134E8TC">standing wave</a> around a <a href="/facts/Atomic_nucleus/orpIm5Xl"> nucleus</a>. An example of a standing wave is a violin string, which is fixed at both ends and can be made to vibrate. The waves created by a stringed instrument appear to oscillate in place, moving from crest to trough in an up-and-down motion. The wavelength of a standing wave is related to the length of the vibrating object and the boundary conditions. For example, because the violin string is fixed at both ends, it can carry standing waves of wavelengths 
 
 
 
 
 
 
 2
 l
 
 n
 
 
 
 
 {\textstyle {\frac {2l}{n}}}
 
, where l is the length and n is a positive integer. De Broglie suggested that the allowed electron orbits were those for which the circumference of the orbit would be an integer number of wavelengths. The electron's wavelength, therefore, determines that only Bohr orbits of certain distances from the nucleus are possible. In turn, at any distance from the nucleus smaller than a certain value, it would be impossible to establish an orbit. The minimum possible distance from the nucleus is called the Bohr radius.<a class="footnote-ref" id="fnref:50" href="#fn:50">50</a> De Broglie's treatment of the Bohr atom was ultimately unsuccessful, but his hypothesis served as a starting point for Schrödinger's wave equation.
Matter behaving as a wave was first demonstrated experimentally: a beam of electrons can exhibit <a href="/facts/Diffraction/Mk80xXHT">diffraction</a>, just like a beam of light or a water wave. Three years after de Broglie published his hypothesis two different groups demonstrated electron diffraction. At the <a href="/facts/University_of_Aberdeen/F6X2yVXk">University of Aberdeen</a>, <a href="/facts/George_Paget_Thomson/Mmk3oA0A">George Paget Thomson</a> and Alexander Reid passed a beam of electrons through a thin celluloid film, then later metal films, and observed the predicted interference patterns. (Alexander Reid, who was Thomson's graduate student, performed the first experiments but he died soon after in a motorcycle accident<a class="footnote-ref" id="fnref:51" href="#fn:51">51</a> and is rarely mentioned.) At <a href="/facts/Bell_Labs/fKP5Gk0H">Bell Labs</a>, <a href="/facts/Clinton_Joseph_Davisson/q9V3p4RQ">Clinton Joseph Davisson</a> and <a href="/facts/Lester_Halbert_Germer/xhwA4oxz">Lester Halbert Germer</a> reflected an electron beam from a nickel sample in their experiment, observing well-defined beams predicted by wave models returning from the crystal.<a class="footnote-ref" id="fnref:52" href="#fn:52">52</a>: II:218  De Broglie was awarded the Nobel Prize in Physics in 1929 for his hypothesis;<a class="footnote-ref" id="fnref:53" href="#fn:53">53</a> Thomson and Davisson shared the Nobel Prize for Physics in 1937 for their experimental work.<a class="footnote-ref" id="fnref:54" href="#fn:54">54</a>

<h2 id="development-of-modern-quantum-mechanics">Development of modern quantum mechanics</h2>
The end of the first era of quantum mechanics was triggered by de Broglie's publication of his hypothesis of <a href="/facts/Matter_wave/Rpszb8f1">matter waves</a><a class="footnote-ref" id="fnref:55" href="#fn:55">55</a>: 268  leading to not just one new quantum theory but two. Almost simultaneously, the German physicists <a href="/facts/Werner_Heisenberg/n4qzYvj4">Werner Heisenberg</a>, <a href="/facts/Max_Born/6VnUDWhA">Max Born</a>, and <a href="/facts/Pascual_Jordan/YNLoGJ5d">Pascual Jordan</a><a class="footnote-ref" id="fnref:56" href="#fn:56">56</a><a class="footnote-ref" id="fnref:57" href="#fn:57">57</a> developed <a href="/facts/Matrix_mechanics/nJxC4pKP">matrix mechanics</a> and the Austrian physicist Erwin Schrödinger invented <a href="/facts/Schr%25C3%25B6dinger_equation/3csgSIWF">wave mechanics</a>.<a class="footnote-ref" id="fnref:58" href="#fn:58">58</a> Schrödinger subsequently showed that the two approaches were equivalent. 
The first applications of quantum mechanics to physical systems were the algebraic determination of the hydrogen spectrum by <a href="/facts/Wolfgang_Pauli/Ugk4ubXk">Wolfgang Pauli</a><a class="footnote-ref" id="fnref:59" href="#fn:59">59</a> and the treatment of diatomic molecules by <a href="/facts/Lucy_Mensing/5mjHKtLW">Lucy Mensing</a>.<a class="footnote-ref" id="fnref:60" href="#fn:60">60</a>
Accurate predictions of the absorption spectrum of hydrogen ensured wide acceptance of the new quantum theory.<a class="footnote-ref" id="fnref:61" href="#fn:61">61</a>: 275 

<h3>Matrix mechanics</h3>
Main article: <a href="/facts/Matrix_mechanics/nJxC4pKP">Matrix mechanics</a> See also: <a href="/facts/Umdeutung_paper/PREv5Fxf">Umdeutung paper</a>
In 1925, Werner Heisenberg attempted to solve one of the problems that the Bohr model left unanswered, explaining the intensities of the different lines in the hydrogen emission spectrum. Through a series of mathematical analogies, he wrote out the quantum-mechanical analog for the classical computation of intensities.<a class="footnote-ref" id="fnref:62" href="#fn:62">62</a> Shortly afterward, Heisenberg's colleague Max Born realized that Heisenberg's method of calculating the probabilities for transitions between the different energy levels could best be expressed by using the mathematical concept of <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrices</a>.
Heisenberg formulated an early version of the <a href="/facts/Uncertainty_principle/UUSoSp4T">uncertainty principle</a> in 1927, analyzing a <a href="/facts/Thought_experiment/GXlr0lz9">thought experiment</a> where one attempts to <a href="/facts/Heisenberg%2527s_microscope/TpC9ww35">measure an electron's position and momentum simultaneously</a>. However, Heisenberg did not give precise mathematical definitions of what the "uncertainty" in these measurements meant, a step that would be taken soon after by <a href="/facts/Earle_Hesse_Kennard/k37kqkAo">Earle Hesse Kennard</a>, Wolfgang Pauli, and <a href="/facts/Hermann_Weyl/4C5HhyGU">Hermann Weyl</a>.<a class="footnote-ref" id="fnref:63" href="#fn:63">63</a><a class="footnote-ref" id="fnref:64" href="#fn:64">64</a>

<h3>Schrödinger and the wave mechanics</h3>
See also: <a href="/facts/History_of_variational_principles_in_physics/xmhBD9GQ">History of variational principles in physics</a>
In the first half of 1926, building on de Broglie's hypothesis, Erwin Schrödinger developed the equation that describes the behavior of a quantum-mechanical wave.<a class="footnote-ref" id="fnref:65" href="#fn:65">65</a> The mathematical model, called the Schrödinger equation after its creator, is central to quantum mechanics, defines the permitted stationary states of a quantum system, and describes how the quantum state of a physical system changes in time.<a class="footnote-ref" id="fnref:66" href="#fn:66">66</a> The wave itself is described by a mathematical function known as a "<a href="/facts/Wave_function/KgM5ykjY">wave function</a>". Schrödinger said that the wave function provides the "means for predicting the probability of measurement results".<a class="footnote-ref" id="fnref:67" href="#fn:67">67</a>
Schrödinger was able to calculate the energy levels of hydrogen by treating a hydrogen atom's electron as a classical wave, moving in a well of the electrical potential created by the proton. This calculation accurately reproduced the energy levels of the Bohr model.
In May 1926, Schrödinger proved that Heisenberg's <a href="/facts/Matrix_mechanics/nJxC4pKP">matrix mechanics</a> and his own wave mechanics made the same predictions about the properties and behavior of the electron; mathematically, the two theories had an underlying common form. Yet the two men disagreed on the interpretation of their mutual theory. For instance, Heisenberg accepted the theoretical prediction of jumps of electrons between orbitals in an atom,<a class="footnote-ref" id="fnref:68" href="#fn:68">68</a> but Schrödinger hoped that a theory based on continuous wave-like properties could avoid what he called (as paraphrased by <a href="/facts/Wilhelm_Wien/Fm4W3S11">Wilhelm Wien</a>) "this nonsense about quantum jumps".<a class="footnote-ref" id="fnref:69" href="#fn:69">69</a> In the end, Heisenberg's approach won out, and quantum jumps were confirmed.<a class="footnote-ref" id="fnref:70" href="#fn:70">70</a>

<h3>Application to the hydrogen atom</h3>
Main article: <a href="/facts/Atomic_orbital_model/tKhgl6mL">Atomic orbital model</a>
Bohr's model of the atom was essentially a planetary one, with the electrons orbiting around the nuclear "sun". However, the uncertainty principle states that an electron cannot simultaneously have an exact location and velocity in the way that a planet does. Instead of classical orbits, electrons are said to inhabit <a href="/facts/Atomic_orbital/tKhgl6mL">atomic orbitals</a>. An orbital is the "cloud" of possible locations in which an electron might be found, a distribution of probabilities rather than a precise location.<a class="footnote-ref" id="fnref:71" href="#fn:71">71</a> Each orbital is three dimensional, rather than the two-dimensional orbit, and is often depicted as a three-dimensional region within which there is a 95 percent probability of finding the electron.<a class="footnote-ref" id="fnref:72" href="#fn:72">72</a>
Schrödinger was able to calculate the energy levels of hydrogen by treating a hydrogen atom's electron as a wave, represented by the "<a href="/facts/Wave_function/KgM5ykjY">wave function</a>" Ψ, in an <a href="/facts/Electric_potential/Nmqm6hm5">electric potential</a> <a href="/facts/Potential_well/EMQxyqDT">well</a>, V, created by the proton. The solutions to Schrödinger's equation are distributions of probabilities for electron positions and locations. Orbitals have a range of different shapes in three dimensions. The energies of the different orbitals can be calculated, and they accurately match the energy levels of the Bohr model.
Within Schrödinger's picture, each electron has four properties:

<ol><li>An "orbital" designation, indicating whether the particle-wave is one that is closer to the nucleus with less energy or one that is farther from the nucleus with more energy;</li>
<li>The "shape" of the orbital, spherical or otherwise;</li>
<li>The "inclination" of the orbital, determining the magnetic moment of the orbital around the z-axis.</li>
<li>The "spin" of the electron.</li></ol>
The collective name for these properties is the <a href="/facts/Quantum_state/7jbxd7Dx">quantum state</a> of the electron. The quantum state can be described by giving a number to each of these properties; these are known as the electron's <a href="/facts/Quantum_numbers/AByP6F0y">quantum numbers</a>. The quantum state of the electron is described by its wave function. The Pauli exclusion principle demands that no two electrons within an atom may have the same values of all four numbers. 
The first property describing the orbital is the <a href="/facts/Principal_quantum_number/8SzSWV6w">principal quantum number</a>, n, which is the same as in the Bohr model. n denotes the energy level of each orbital. The possible values for n are integers:

n
        =
        1
        ,
        2
        ,
        3
        …
      
    
    {\displaystyle n=1,2,3\ldots }

The next quantum number, the <a href="/facts/Azimuthal_quantum_number/vHSIzbFC">azimuthal quantum number</a>, denoted l, describes the shape of the orbital. The shape is a consequence of the <a href="/facts/Angular_momentum/7TuSVFxq">angular momentum</a> of the orbital. The angular momentum represents the resistance of a spinning object to speeding up or slowing down under the influence of external force. The azimuthal quantum number represents the orbital angular momentum of an electron around its nucleus. The possible values for l are integers from 0 to n − 1 (where n is the principal quantum number of the electron):

l
        =
        0
        ,
        1
        ,
        …
        ,
        n
        −
        1.
      
    
    {\displaystyle l=0,1,\ldots ,n-1.}

The shape of each orbital is usually referred to by a letter, rather than by its azimuthal quantum number. The first shape (l=0) is denoted by the letter s (a <a href="/facts/Mnemonic/6HfDn0ks">mnemonic</a> being "sphere"). The next shape is denoted by the letter p and has the form of a dumbbell. The other orbitals have more complicated shapes (see <a href="/facts/Atomic_orbital/tKhgl6mL">atomic orbital</a>), and are denoted by the letters d, f, g, etc.
The third quantum number, the <a href="/facts/Magnetic_quantum_number/LvFY0dVV">magnetic quantum number</a>, describes the magnetic moment of the electron, and is denoted by ml (or simply m). The possible values for ml are integers from −l to l (where l is the azimuthal quantum number of the electron):

m
          
            l
          
        
        =
        −
        l
        ,
        −
        (
        l
        −
        1
        )
        ,
        …
        ,
        0
        ,
        …
        ,
        (
        l
        −
        1
        )
        ,
        l
        .
      
    
    {\displaystyle m_{l}=-l,-(l-1),\ldots ,0,\ldots ,(l-1),l.}

The magnetic quantum number measures the component of the angular momentum in a particular direction. The choice of direction is arbitrary; conventionally the z-direction is chosen.
The fourth quantum number, the <a href="/facts/Spin_quantum_number/5Nh2H8gr">spin quantum number</a> (pertaining to the "orientation" of the electron's spin) is denoted ms, with values +1⁄2 or −1⁄2.
The chemist <a href="/facts/Linus_Pauling/cBNBzs5c">Linus Pauling</a> wrote, by way of example:

<blockquote>In the case of a <a href="/facts/Helium/yRul93TG">helium</a> atom with two electrons in the 1s orbital, the Pauli Exclusion Principle requires that the two electrons differ in the value of one quantum number. Their values of n, l, and ml are the same. Accordingly they must differ in the value of ms, which can have the value of +1⁄2 for one electron and −1⁄2 for the other."<a class="footnote-ref" id="fnref:73" href="#fn:73">73</a></blockquote>
It is the underlying structure and symmetry of atomic orbitals, and the way that electrons fill them, that leads to the organization of the <a href="/facts/Periodic_table/umdGIfUb">periodic table</a>. The way the atomic orbitals on different atoms combine to form <a href="/facts/Molecular_orbital/0dP30jaa">molecular orbitals</a> determines the structure and strength of chemical bonds between atoms.
The field of <a href="/facts/Quantum_chemistry/H9AXV0lx">quantum chemistry</a> was pioneered by physicists <a href="/facts/Walter_Heitler/nhLXAQQ4">Walter Heitler</a> and <a href="/facts/Fritz_London/9NvJ4MR7">Fritz London</a>, who published a study of the <a href="/facts/Covalent_bond/EzMLf3Pz">covalent bond</a> of the <a href="/facts/Hydrogen_molecule/BoYHjl0J">hydrogen molecule</a> in 1927. Quantum chemistry was subsequently developed by a large number of workers, including the American theoretical chemist <a href="/facts/Linus_Pauling/cBNBzs5c">Linus Pauling</a> at <a href="/facts/Caltech/3FPcp7BL">Caltech</a>, and <a href="/facts/John_C._Slater/nfqa6fbn">John C. Slater</a> into various theories such as Molecular Orbital Theory or Valence Theory.

<h3>Dirac, relativity, and development of the formal methods</h3>
Starting around 1927, Paul Dirac began the process of unifying quantum mechanics with <a href="/facts/Special_relativity/vsFFc63E">special relativity</a> by proposing the <a href="/facts/Dirac_equation/DzFaXS4p">Dirac equation</a> for the electron. The Dirac equation achieves the relativistic description of the wavefunction of an electron that Schrödinger failed to obtain. It predicts electron spin and led Dirac to predict the existence of the <a href="/facts/Positron/HgV4zBzA">positron</a>. He also pioneered the use of operator theory, including the influential <a href="/facts/Bra%25E2%2580%2593ket_notation/NDlKsaRh">bra–ket notation</a>, as described in his famous 1930 textbook. During the same period, Hungarian polymath <a href="/facts/John_von_Neumann/aUk6urof">John von Neumann</a> formulated the rigorous mathematical basis for quantum mechanics as the theory of linear operators on Hilbert spaces, as described in his <a href="/facts/Mathematical_Foundations_of_Quantum_Mechanics/Czkz1BAj">likewise famous 1932 textbook</a>. These, like many other works from the founding period, still stand, and remain widely used.

<h3>Copenhagen interpretation</h3>
Main article: <a href="/facts/Copenhagen_interpretation/DvMFrYJa">Copenhagen interpretation</a>

Bohr, Heisenberg, and others tried to explain what these experimental results and mathematical models really mean. The term <a href="/facts/Copenhagen_interpretation/DvMFrYJa">Copenhagen interpretation</a> has been applied to their views in retrospect, glossing over differences among them.<a class="footnote-ref" id="fnref:74" href="#fn:74">74</a><a class="footnote-ref" id="fnref:75" href="#fn:75">75</a><a class="footnote-ref" id="fnref:76" href="#fn:76">76</a><a class="footnote-ref" id="fnref:77" href="#fn:77">77</a><a class="footnote-ref" id="fnref:78" href="#fn:78">78</a><a class="footnote-ref" id="fnref:79" href="#fn:79">79</a> While no definitive statement of "the" Copenhagen interpretation exists, the following ideas are widely seen as characteristic of it.

<ol><li>A system is completely described by a quantum state (Heisenberg)</li>
<li>How the quantum state changes over time is given by a wave equation, the <a href="/facts/Schr%25C3%25B6dinger_equation/3csgSIWF">Schrödinger equation</a> imparting wave characteristics to light and matter.</li>
<li>Atomic interactions are discontinuous (Planck referred to a "<a href="/facts/Planck_constant/qGHAe3qq">quantum of action</a>").</li>
<li>The description of nature is essentially probabilistic. The probability of an event—for example, where on the screen a particle shows up in the double-slit experiment—is related to the square of the absolute value of the amplitude of its wave function. (<a href="/facts/Born_rule/XAsF5Ndf">Born rule</a>, due to <a href="/facts/Max_Born/6VnUDWhA">Max Born</a>, which gives a physical meaning to the wave function in the Copenhagen interpretation: the <a href="/facts/Probability_amplitude/ryPgJvs8">probability amplitude</a>)</li>
<li>The values of incompatible pairs of properties of the system cannot be known at the same time. (Heisenberg's <a href="/facts/Uncertainty_principle/UUSoSp4T">uncertainty principle</a>)</li>
<li>Matter, like light, exhibits a wave-particle duality. An experiment can demonstrate the particle-like properties of matter, or its wave-like properties; but not both at the same time. (<a href="/facts/Complementarity_principle/GFpfyVs2">Complementarity principle</a> due to Bohr<a class="footnote-ref" id="fnref:80" href="#fn:80">80</a>)</li>
<li>Measuring devices are essentially classical devices and measure classical properties such as position and momentum.</li>
<li>The quantum mechanical description of large systems should closely approximate the classical description. (<a href="/facts/Correspondence_principle/F4RFL8sR">Correspondence principle</a> of Bohr and Heisenberg)</li></ol>
<h2 id="quantum-field-theory">Quantum field theory</h2>
Beginning in 1927, researchers attempted to apply quantum mechanics to fields instead of single particles, resulting in quantum field theories. Early workers in this area include Pauli, <a href="/facts/Paul_Dirac/6bt5yRdk">Paul Dirac</a>, <a href="/facts/Victor_Weisskopf/jocTeNnB">Victor Weisskopf</a>, and <a href="/facts/Pascual_Jordan/YNLoGJ5d">Paul Jordan</a>. This area of research culminated in the formulation of <a href="/facts/Quantum_electrodynamics/zPteAr6G">quantum electrodynamics</a> by <a href="/facts/Richard_Feynman/32vGFrtB">Richard Feynman</a>, <a href="/facts/Freeman_Dyson/kSRxTh2r">Freeman Dyson</a>, <a href="/facts/Julian_Schwinger/BdepoI1r">Julian Schwinger</a>, and <a href="/facts/Shin%2527ichir%25C5%258D_Tomonaga/2wqqyq8g">Shin'ichiro Tomonaga</a> during the 1940s. Quantum electrodynamics describes a quantum theory of electrons, <a href="/facts/Positron/HgV4zBzA">positrons</a>, and the <a href="/facts/Electromagnetic_field/MacraS8y">electromagnetic field</a>, and served as a model for subsequent <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theories</a>.<a class="footnote-ref" id="fnref:81" href="#fn:81">81</a><a class="footnote-ref" id="fnref:82" href="#fn:82">82</a><a class="footnote-ref" id="fnref:83" href="#fn:83">83</a>

The theory of <a href="/facts/Quantum_chromodynamics/3cA2ctyb">quantum chromodynamics</a> was formulated beginning in the early 1960s. The theory as we know it today was formulated by <a href="/facts/Hugh_David_Politzer/Xlo8AGLD">Hugh David Politzer</a>, <a href="/facts/David_Gross/W76ShB3u">David Gross</a> and <a href="/facts/Frank_Wilczek/EnrB8uUn">Frank Wilczek</a> in 1975.
Building on pioneering work by Schwinger, <a href="/facts/Peter_Higgs/zGvqlC99">Peter Higgs</a> and <a href="/facts/Jeffrey_Goldstone/1k9Vw5fd">Jeffrey Goldstone</a>, the physicists <a href="/facts/Sheldon_Glashow/KNS7qjog">Sheldon Glashow</a>, <a href="/facts/Steven_Weinberg/G61D6kJw">Steven Weinberg</a> and <a href="/facts/Abdus_Salam/M4GNh8dE">Abdus Salam</a> independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single <a href="/facts/Electroweak_force/QATz4dYF">electroweak force</a>, for which they received the 1979 Nobel Prize in Physics.

<h2 id="quantum-information">Quantum information</h2>
See also: <a href="/facts/Timeline_of_quantum_computing_and_communication/s1pp1CP2">Timeline of quantum computing and communication</a>
<a href="/facts/Quantum_information_science/JDuxpHp8">Quantum information science</a> developed in the latter decades of the 20th century, beginning with theoretical results like <a href="/facts/Holevo%2527s_theorem/uUXVmYER">Holevo's theorem</a>, the concept of generalized measurements or <a href="/facts/POVM/ouBuwcck">POVMs</a>, the proposal of <a href="/facts/Quantum_key_distribution/aJ4aQ6yw">quantum key distribution</a> by <a href="/facts/BB84/8d2G3lfC">Bennett and Brassard</a> in 1984, and <a href="/facts/Shor%2527s_algorithm/9JwEtznC">Shor's algorithm</a> in 1994.

<h2 id="founding-experiments">Founding experiments</h2>
<ul><li><a href="/facts/Thomas_Young_(scientist)/X4RtR47L">Thomas Young</a>'s <a href="/facts/Double-slit_experiment/TR8zwEcy">double-slit experiment</a> demonstrating the wave nature of light. (c. 1801)</li>
<li><a href="/facts/Henri_Becquerel/wN7DSsVL">Henri Becquerel</a> discovers <a href="/facts/Radioactivity/Ya6FVjt4">radioactivity</a>. (1896)</li>
<li><a href="/facts/J._J._Thomson/Y4jyndJF">J. J. Thomson</a>'s cathode ray tube experiments (discovers the electron and its negative charge). (1897)</li>
<li>The study of <a href="/facts/Black-body_radiation/f0fHghDy">black-body radiation</a> between 1850 and 1900, which could not be explained without quantum concepts.</li>
<li>The <a href="/facts/Photoelectric_effect/gIDcdm5U">photoelectric effect</a>: Einstein explained this in 1905 (and later received a Nobel prize for it) using the concept of photons, particles of light with quantized energy.</li>
<li><a href="/facts/Robert_Millikan/rrWMCh2y">Robert Millikan</a>'s <a href="/facts/Oil-drop_experiment/C2BBYkKh">oil-drop experiment</a>, which showed that <a href="/facts/Electric_charge/xxsBfmlB">electric charge</a> occurs as <a href="/facts/Quantum/4x5QTxGB">quanta</a> (whole units). (1909)</li>
<li><a href="/facts/Ernest_Rutherford/hjjMEskl">Ernest Rutherford</a>'s <a href="/facts/Geiger%25E2%2580%2593Marsden_experiment/cmgI1Ha9">gold foil experiment</a> disproved the plum pudding model of the <a href="/facts/Atom/69syB8dH">atom</a> which suggested that the mass and positive charge of the atom are almost uniformly distributed. This led to the planetary model of the atom (1911).</li>
<li><a href="/facts/James_Franck/SooVoCUz">James Franck</a> and <a href="/facts/Gustav_Ludwig_Hertz/uudggEgb">Gustav Hertz's</a> <a href="/facts/Franck%25E2%2580%2593Hertz_experiment/I0RYd51S">electron collision experiment</a> shows that energy absorption by mercury atoms is quantized. (1914)</li>
<li><a href="/facts/Otto_Stern/9eP2K5rB">Otto Stern</a> and <a href="/facts/Walther_Gerlach/qEjsbn0c">Walther Gerlach</a> conduct the <a href="/facts/Stern%25E2%2580%2593Gerlach_experiment/PCWPE56v">Stern–Gerlach experiment</a>, which demonstrates the quantized nature of particle <a href="/facts/Spin_(physics)/4Jvp7e8P">spin</a>. (1920)</li>
<li><a href="/facts/Arthur_Compton/FrNYLBj4">Arthur Compton</a> with <a href="/facts/Compton_scattering/Q98Ty8rz">Compton scattering</a> experiment (1923)</li>
<li><a href="/facts/Clinton_Davisson/q9V3p4RQ">Clinton Davisson</a> and <a href="/facts/Lester_Germer/xhwA4oxz">Lester Germer</a> demonstrate the wave nature of the electron<a class="footnote-ref" id="fnref:84" href="#fn:84">84</a> in the <a href="/facts/Electron_diffraction/IlFzQyVu">electron diffraction</a> experiment. (1927)</li>
<li><a href="/facts/Carl_David_Anderson/rIMqD9ax">Carl David Anderson</a> with the discovery positron (1932), validated Paul Dirac's theoretical prediction of this particle (1928)</li>
<li><a href="/facts/Willis_Lamb/srfCyHko">Lamb</a>–<a href="/facts/Robert_Retherford/N12oAFeG">Retherford</a> experiment discovered <a href="/facts/Lamb_shift/p4rqJV2j">Lamb shift</a> (1947), which led to the development of quantum electrodynamics.</li>
<li><a href="/facts/Clyde_L._Cowan/kdySD9zb">Clyde L. Cowan</a> and <a href="/facts/Frederick_Reines/sdWH4hNg">Frederick Reines</a> confirm the existence of the <a href="/facts/Neutrino/yGWVfSg2">neutrino</a> in the <a href="/facts/Neutrino_experiment/2XaJzDRC">neutrino experiment</a>. (1955)</li>
<li><a href="/facts/Claus_J%25C3%25B6nsson/e0qpLIK4">Claus Jönsson</a>'s double-slit experiment with electrons. (1961)</li>
<li>The <a href="/facts/Quantum_Hall_effect/yK3zcCgu">quantum Hall effect</a>, discovered in 1980 by <a href="/facts/Klaus_von_Klitzing/pDnImSAK">Klaus von Klitzing</a>. The quantized version of the <a href="/facts/Hall_effect/4r86ffPr">Hall effect</a> has allowed for the definition of a new practical standard for <a href="/facts/Electrical_resistance/hxSt0UAj">electrical resistance</a> and for an extremely precise independent determination of the <a href="/facts/Fine-structure_constant/zyzpmTJV">fine-structure constant</a>.</li>
<li>The <a href="/facts/Bell_test_experiments/YDKYlhGa">experimental verification</a> of <a href="/facts/Quantum_entanglement/afzslwN0">quantum entanglement</a> by <a href="/facts/John_Clauser/o6CjMy76">John Clauser</a> and <a href="/facts/Stuart_Freedman/Cy0dT149">Stuart Freedman</a>. (1972)</li>
<li>The <a href="/facts/Mach%25E2%2580%2593Zehnder_interferometer/gP0B1j0w">Mach–Zehnder interferometer</a> experiment conducted by <a href="/facts/Paul_Kwiat/wFpu7uPs">Paul Kwiat</a>, Harold Wienfurter, Thomas Herzog, <a href="/facts/Anton_Zeilinger/bJoKANHh">Anton Zeilinger</a>, and Mark Kasevich, providing <a href="/facts/Elitzur%25E2%2580%2593Vaidman_bomb-testing_problem/P6F4pDTo">experimental verification of the Elitzur–Vaidman bomb tester</a>, proving <a href="/facts/Interaction-free_measurement/zqEgYGxL">interaction-free measurement</a> is possible. (1994)</li></ul>
<h2 id="see-also">See also</h2>
<ul>
<li>History of science portal</li><li>Nuclear technology portal</li><li>Physics portal</li></ul>

<ul><li><a href="/facts/Golden_age_of_physics/cBvtwECk">Golden age of physics</a></li>
<li><a href="/facts/Einstein%2527s_thought_experiments/ptuoP6uG">Einstein's thought experiments</a></li>
<li><a href="/facts/History_of_quantum_field_theory/9K6v1WbU">History of quantum field theory</a></li>
<li><a href="/facts/History_of_chemistry/toCwmnGW">History of chemistry</a></li>
<li><a href="/facts/History_of_molecular_theory/78Qhe96u">History of molecular theory</a></li>
<li><a href="/facts/History_of_thermodynamics/fXM5hhjt">History of thermodynamics</a></li>
<li><a href="/facts/Timeline_of_atomic_and_subatomic_physics/jM3hwrwh">Timeline of atomic and subatomic physics</a></li></ul>

<h2 id="further-reading">Further reading</h2>
<ul><li>Bacciagaluppi, Guido; <a href="/facts/Antony_Valentini/eChxF95R">Valentini, Antony</a> (2009), Quantum theory at the crossroads: reconsidering the 1927 Solvay conference, Cambridge, UK: Cambridge University Press, p. 9184, <a href="/facts/ArXiv_(identifier)/H6EtgnBe">arXiv</a>:<a href="https://arxiv.org/abs/quant-ph/0609184">quant-ph/0609184</a>, <a href="/facts/Bibcode_(identifier)/9HtdQSGB">Bibcode</a>:<a href="https://ui.adsabs.harvard.edu/abs/2006quant.ph..9184B">2006quant.ph..9184B</a>, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-521-81421-8, <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/227191829">227191829</a></li>
<li>Bernstein, Jeremy (2009), <a href="https://books.google.com/books?id=j0Me3brYOL0C">Quantum Leaps</a>, Cambridge, Massachusetts: Belknap Press of Harvard University Press, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-674-03541-6</li>
<li>Greenberger, Daniel, <a href="/facts/Klaus_Hentschel/QYnpFbbo">Hentschel, Klaus</a>, Weinert, Friedel (Eds.) <a href="https://www.springer.com/us/book/9783540706229">Compendium of Quantum Physics</a>. Concepts, Experiments, History and Philosophy, New York: Springer, 2009. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3-540-70626-7.</li>
<li><a href="/facts/Max_Jammer/LdkDemCF">Jammer, Max</a> (1966), The conceptual development of quantum mechanics, New York: McGraw-Hill, <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/534562">534562</a></li>
<li><a href="/facts/Max_Jammer/LdkDemCF">Jammer, Max</a> (1974), <a href="https://archive.org/details/philosophyofquan0000jamm">The philosophy of quantum mechanics: The interpretations of quantum mechanics in historical perspective</a>, New York: Wiley, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-471-43958-4, <a href="/facts/OCLC_(identifier)/Yqad8waq">OCLC</a> <a href="https://search.worldcat.org/oclc/969760">969760</a></li>
<li>A. Whitaker. The New Quantum Age: From Bell's Theorem to Quantum Computation and Teleportation, Oxford University Press, 2011, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-19-958913-5</li>
<li>Stephen Hawking. The Dreams that Stuff is Made of, Running Press, 2011, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-76-243434-3</li>
<li>A. Douglas Stone. Einstein and the Quantum, the Quest of the Valiant Swabian, Princeton University Press, 2006.</li></ul>
<h2 id="external-links">External links</h2>

Wikiquote has quotations related to History of quantum mechanics.

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Whittaker, Edmund T. (1989). A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 (Repr ed.). New York: Dover Publ. ISBN 978-0-486-26126-3. <a href="978-0-486-26126-3" target="_blank">978-0-486-26126-3</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Max Born, My Life: Recollections of a Nobel Laureate, Taylor & Francis, London, 1978. ("We became more and more convinced that a radical change of the foundations of physics was necessary, i.e., a new kind of mechanics for which we used the term quantum mechanics. This word appears for the first time in physical literature in a paper of mine ...") <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Fedak, William A.; Prentis, Jeffrey J. (2009-02-01). "The 1925 Born and Jordan paper "On quantum mechanics"" (PDF). Am. J. Phys. 77 (2). American Association of Physics Teachers: 128–139. Bibcode:2009AmJPh..77..128F. doi:10.1119/1.3009634. ISSN 0002-9505. <a href="https://people.isy.liu.se/icg/jalar/kurser/QF/references/onBornJordan1925.pdf" target="_blank">https://people.isy.liu.se/icg/jalar/kurser/QF/references/onBornJordan1925.pdf</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Born, M.; Jordan, P. (27 September 1925). "Zur Quantenmechanik" (PDF). Z. Physik (in German). 34. Gottingen: 858–888. Retrieved 29 May 2025 – via Qwant: Universität Tübingen.{{cite journal}}: CS1 maint: date and year (link) <a href="https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/born_jordan_ZPhys_34_858_1925.pdf" target="_blank">https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/born_jordan_ZPhys_34_858_1925.pdf</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Whittaker, Edmund T. (1989). A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 (Repr ed.). New York: Dover Publ. ISBN 978-0-486-26126-3. <a href="978-0-486-26126-3" target="_blank">978-0-486-26126-3</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Young, Thomas (1804). "Bakerian Lecture: Experiments and calculations relative to physical optics". Philosophical Transactions of the Royal Society. 94: 1–16. Bibcode:1804RSPT...94....1Y. doi:10.1098/rstl.1804.0001. S2CID 110408369. <a href="https://books.google.com/books?id=7AZGAAAAMAAJ&pg=PA1" target="_blank">https://books.google.com/books?id=7AZGAAAAMAAJ&pg=PA1</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">Buchwald, Jed (1989). The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century. Chicago: University of Chicago Press. ISBN 978-0-226-07886-1. OCLC 18069573. <a href="978-0-226-07886-1" target="_blank">978-0-226-07886-1</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">Whittaker, Edmund T. (1989). A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 (Repr ed.). New York: Dover Publ. ISBN 978-0-486-26126-3. <a href="978-0-486-26126-3" target="_blank">978-0-486-26126-3</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">Feynman, Richard; Leighton, Robert; Sands, Matthew (1964). The Feynman Lectures on Physics. Vol. 1. California Institute of Technology. ISBN 978-0201500646. Retrieved 30 September 2021. {{cite book}}: ISBN / Date incompatibility (help) <a href="978-0201500646" target="_blank">978-0201500646</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">Pojman, Paul (2020), "Ernst Mach", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Winter 2020 ed.), Metaphysics Research Lab, Stanford University, retrieved 2021-09-30 <a href="https://plato.stanford.edu/archives/win2020/entries/ernst-mach/" target="_blank">https://plato.stanford.edu/archives/win2020/entries/ernst-mach/</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">"The Feynman Lectures on Physics Vol. I Ch. 40: The Principles of Statistical Mechanics". www.feynmanlectures.caltech.edu. Retrieved 2024-03-10. <a href="https://www.feynmanlectures.caltech.edu/I_40.html" target="_blank">https://www.feynmanlectures.caltech.edu/I_40.html</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">Whittaker, Edmund T. (1989). A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 (Repr ed.). New York: Dover Publ. ISBN 978-0-486-26126-3. <a href="978-0-486-26126-3" target="_blank">978-0-486-26126-3</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">Helge Kragh (Oct. 2010). Before Bohr: Theories of atomic structure 1850-1913. RePoSS: Research Publications on Science Studies 10. Aarhus: Centre for Science Studies, University of Aarhus. <a href="https://css.au.dk/fileadmin/reposs/reposs-010.pdf" target="_blank">https://css.au.dk/fileadmin/reposs/reposs-010.pdf</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">Heilbron, John L. (1968). "The Scattering of α and β Particles and Rutherford's Atom". Archive for History of Exact Sciences. 4 (4): 247–307. doi:10.1007/BF00411591. ISSN 0003-9519. JSTOR 41133273. <a href="https://www.jstor.org/stable/41133273" target="_blank">https://www.jstor.org/stable/41133273</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
<li id="fn:15">Whittaker, Edmund T. (1989). A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 (Repr ed.). New York: Dover Publ. ISBN 978-0-486-26126-3. <a href="978-0-486-26126-3" target="_blank">978-0-486-26126-3</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></li>
<li id="fn:16">Whittaker, Edmund T. (1989). A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 (Repr ed.). New York: Dover Publ. ISBN 978-0-486-26126-3. <a href="978-0-486-26126-3" target="_blank">978-0-486-26126-3</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></li>
<li id="fn:17">This result was published (in German) as Planck, Max (1901). "Ueber das Gesetz der Energieverteilung im Normalspectrum". Annalen der Physik. 309 (3): 553–63. Bibcode:1901AnP...309..553P. doi:10.1002/andp.19013090310.. English translation: "On the Law of Distribution of Energy in the Normal Spectrum". Archived from the original on 18 April 2008. <a href="/wiki/Max_Planck" target="_blank">/wiki/Max_Planck</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></li>
<li id="fn:18">"The Nobel Prize in Physics 1918". Nobel Foundation. Retrieved 2009-08-01. <a href="http://nobelprize.org/nobel_prizes/physics/laureates/1918/" target="_blank">http://nobelprize.org/nobel_prizes/physics/laureates/1918/</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></li>
<li id="fn:19">Kragh, Helge (1 December 2000). "Max Planck: the reluctant revolutionary". PhysicsWorld.com. Archived from the original on 1 April 2012. Retrieved 7 December 2009. <a href="https://web.archive.org/web/20120401221617/http://physicsworld.com/cws/article/print/373" target="_blank">https://web.archive.org/web/20120401221617/http://physicsworld.com/cws/article/print/373</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></li>
<li id="fn:20">Whittaker, Edmund T. (1989). A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 (Repr ed.). New York: Dover Publ. ISBN 978-0-486-26126-3. <a href="978-0-486-26126-3" target="_blank">978-0-486-26126-3</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></li>
<li id="fn:21">Wheaton, Bruce R. (1978). "Philipp Lenard and the Photoelectric Effect, 1889-1911". Historical Studies in the Physical Sciences. 9: 299–322. doi:10.2307/27757381. JSTOR 27757381. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></li>
<li id="fn:22">Hawking, Stephen (November 6, 2001) [November 5, 2001]. The Universe in a Nutshell. Vol. 55. Impey, C.D. Bantam Spectra (published April 2002). p. 80~. doi:10.1063/1.1480788. ISBN 978-0553802023. S2CID 120382028. Archived from the original on September 21, 2020. Retrieved December 14, 2020 – via Random House Audiobooks. Alt URL <a href="978-0553802023" target="_blank">978-0553802023</a> <a href="#fnref:22" class="footnote-back-ref">↩</a></li>
<li id="fn:23">Einstein, Albert (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt". Annalen der Physik. 17 (6): 132–48. Bibcode:1905AnP...322..132E. doi:10.1002/andp.19053220607., translated into English as On a Heuristic Viewpoint Concerning the Production and Transformation of Light Archived 11 June 2009 at the Wayback Machine <a href="/wiki/Albert_Einstein" target="_blank">/wiki/Albert_Einstein</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></li>
<li id="fn:24">Folsing, Albrecht (1997), Albert Einstein: A Biography, trans. Ewald Osers, Viking <a href="/wiki/Ewald_Osers" target="_blank">/wiki/Ewald_Osers</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></li>
<li id="fn:25">Einstein, Albert (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt". Annalen der Physik. 17 (6): 132–48. Bibcode:1905AnP...322..132E. doi:10.1002/andp.19053220607., translated into English as On a Heuristic Viewpoint Concerning the Production and Transformation of Light Archived 11 June 2009 at the Wayback Machine <a href="/wiki/Albert_Einstein" target="_blank">/wiki/Albert_Einstein</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></li>
<li id="fn:26">Taylor, J. R.; Zafiratos, C. D.; Dubson, M. A. (2004). Modern Physics for Scientists and Engineers. Prentice Hall. pp. 127–29. ISBN 0135897890. <a href="0135897890" target="_blank">0135897890</a> <a href="#fnref:26" class="footnote-back-ref">↩</a></li>
<li id="fn:27">"The Nobel Prize in Physics 1921". The Nobel Foundation. <a href="https://www.nobelprize.org/prizes/physics/1921/summary/" target="_blank">https://www.nobelprize.org/prizes/physics/1921/summary/</a> <a href="#fnref:27" class="footnote-back-ref">↩</a></li>
<li id="fn:28">Compton, Arthur (1923). "A quantum theory of the scattering of X-rays by light elements". Physical Review. 21 (5): 483–502. Bibcode:1923PhRv...21..483C. doi:10.1103/PhysRev.21.483. Archived from the original on 2018-01-29. Retrieved 2020-11-08. <a href="/wiki/Arthur_Compton" target="_blank">/wiki/Arthur_Compton</a> <a href="#fnref:28" class="footnote-back-ref">↩</a></li>
<li id="fn:29">"The Nobel Prize in Physics 1927". The Nobel Foundation. <a href="https://www.nobelprize.org/prizes/physics/1927/summary/" target="_blank">https://www.nobelprize.org/prizes/physics/1927/summary/</a> <a href="#fnref:29" class="footnote-back-ref">↩</a></li>
<li id="fn:30">"December 18, 1926: Gilbert Lewis coins "photon" in letter to Nature". www.aps.org. Archived from the original on 2019-05-02. Retrieved 2019-03-09. <a href="https://www.aps.org/publications/apsnews/201212/physicshistory.cfm" target="_blank">https://www.aps.org/publications/apsnews/201212/physicshistory.cfm</a> <a href="#fnref:30" class="footnote-back-ref">↩</a></li>
<li id="fn:31">Heilbron, John L. (1968). "The Scattering of α and β Particles and Rutherford's Atom". Archive for History of Exact Sciences. 4 (4): 247–307. doi:10.1007/BF00411591. ISSN 0003-9519. JSTOR 41133273. <a href="https://www.jstor.org/stable/41133273" target="_blank">https://www.jstor.org/stable/41133273</a> <a href="#fnref:31" class="footnote-back-ref">↩</a></li>
<li id="fn:32">Lightman, Alan (2005). The Discoveries. p. 155. <a href="/wiki/Alan_Lightman" target="_blank">/wiki/Alan_Lightman</a> <a href="#fnref:32" class="footnote-back-ref">↩</a></li>
<li id="fn:33">McEvoy, J. P.; Zarate, O. (2004). Introducing Quantum Theory. Totem Books. pp. 70–89, [89]. ISBN 1840465778. <a href="1840465778" target="_blank">1840465778</a> <a href="#fnref:33" class="footnote-back-ref">↩</a></li>
<li id="fn:34">McCormmach, Russell (1 January 1966). "The atomic theory of John William Nicholson". Archive for History of Exact Sciences. 3 (2): 160–184. doi:10.1007/BF00357268. JSTOR 41133258. S2CID 120797894. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:34" class="footnote-back-ref">↩</a></li>
<li id="fn:35">World Book Inc. (2007). "22". World Book Encyclopedia (Electronic reproduction). The World Book encyclopedia. Vol. 22 (3 ed.). Chicago, Illinois: World Book. p. 6. ISBN 978-0716601074. OCLC 894799866. Archived from the original on 30 January 2017. Retrieved December 14, 2020. Alt URL <a href="978-0716601074" target="_blank">978-0716601074</a> <a href="#fnref:35" class="footnote-back-ref">↩</a></li>
<li id="fn:36">Wittke, J.P; Dicke, R.H (June 1, 1961) [1960]. "11". In Holladay, W.G. (ed.). Introduction to Quantum Mechanics (eBook). Vol. 16. Nashville, Tennessee: ADDISON WESLEY LONGMAN INC (published January 1, 1978). p. 10. doi:10.1063/1.3057610. ISBN 978-0201015102. OCLC 53473. Retrieved December 14, 2020 – via Vanderbilt University. {{cite book}}: ISBN / Date incompatibility (help) <a href="978-0201015102" target="_blank">978-0201015102</a> <a href="#fnref:36" class="footnote-back-ref">↩</a></li>
<li id="fn:37">Heilbron, John L.; Kuhn, Thomas S. (1969-01-01). "The Genesis of the Bohr Atom". Historical Studies in the Physical Sciences. 1. University of California Press: vi–290. doi:10.2307/27757291. ISSN 0073-2672. JSTOR 27757291. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:37" class="footnote-back-ref">↩</a></li>
<li id="fn:38">McCormmach, Russell (Spring 1967), "Henri Poincaré and the Quantum Theory", Isis, 58 (1): 37–55, doi:10.1086/350182, S2CID 120934561 <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:38" class="footnote-back-ref">↩</a></li>
<li id="fn:39">Irons, F. E. (August 2001), "Poincaré's 1911–12 proof of quantum discontinuity interpreted as applying to atoms", American Journal of Physics, 69 (8): 879–84, Bibcode:2001AmJPh..69..879I, doi:10.1119/1.1356056 <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:39" class="footnote-back-ref">↩</a></li>
<li id="fn:40">"The Nobel Prize in Physics 1922". The Nobel Foundation. <a href="https://www.nobelprize.org/prizes/physics/1922/summary/" target="_blank">https://www.nobelprize.org/prizes/physics/1922/summary/</a> <a href="#fnref:40" class="footnote-back-ref">↩</a></li>
<li id="fn:41">Friedrich, Bretislav; Herschbach, Dudley (December 2003). "Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics". Physics Today. 56 (12): 53–59. Bibcode:2003PhT....56l..53F. doi:10.1063/1.1650229. ISSN 0031-9228. <a href="https://doi.org/10.1063%2F1.1650229" target="_blank">https://doi.org/10.1063%2F1.1650229</a> <a href="#fnref:41" class="footnote-back-ref">↩</a></li>
<li id="fn:42">Friedrich, Bretislav; Herschbach, Dudley (December 2003). "Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics". Physics Today. 56 (12): 53–59. Bibcode:2003PhT....56l..53F. doi:10.1063/1.1650229. ISSN 0031-9228. <a href="https://doi.org/10.1063%2F1.1650229" target="_blank">https://doi.org/10.1063%2F1.1650229</a> <a href="#fnref:42" class="footnote-back-ref">↩</a></li>
<li id="fn:43">"The Nobel Prize in Physics 1945". The Nobel Foundation. <a href="https://www.nobelprize.org/prizes/physics/1945/summary/" target="_blank">https://www.nobelprize.org/prizes/physics/1945/summary/</a> <a href="#fnref:43" class="footnote-back-ref">↩</a></li>
<li id="fn:44">Baggott, J. E. (2013). The quantum story: a history in 40 moments (Impression: 3 ed.). Oxford: Oxford Univ. Press. ISBN 978-0-19-965597-7. <a href="978-0-19-965597-7" target="_blank">978-0-19-965597-7</a> <a href="#fnref:44" class="footnote-back-ref">↩</a></li>
<li id="fn:45">Pais, Abraham. "George Uhlenbeck and the discovery of electron spin." Physics Today 42.12 (1989): 34-40. <a href="#fnref:45" class="footnote-back-ref">↩</a></li>
<li id="fn:46">Aczel, Amir D., Entanglement, pp. 51ff. (Penguin, 2003) ISBN 978-1551926476 <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:46" class="footnote-back-ref">↩</a></li>
<li id="fn:47">McEvoy, J. P.; Zarate, O. (2004). Introducing Quantum Theory. Totem Books. p. 114. ISBN 1840465778. <a href="1840465778" target="_blank">1840465778</a> <a href="#fnref:47" class="footnote-back-ref">↩</a></li>
<li id="fn:48">Whittaker, Edmund T. (1989). A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 (Repr ed.). New York: Dover Publ. ISBN 978-0-486-26126-3. <a href="978-0-486-26126-3" target="_blank">978-0-486-26126-3</a> <a href="#fnref:48" class="footnote-back-ref">↩</a></li>
<li id="fn:49">Whittaker, Edmund T. (1989). A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 (Repr ed.). New York: Dover Publ. ISBN 978-0-486-26126-3. <a href="978-0-486-26126-3" target="_blank">978-0-486-26126-3</a> <a href="#fnref:49" class="footnote-back-ref">↩</a></li>
<li id="fn:50">McEvoy, J. P.; Zarate, O. (2004). Introducing Quantum Theory. Totem Books. p. 87. ISBN 1840465778. <a href="1840465778" target="_blank">1840465778</a> <a href="#fnref:50" class="footnote-back-ref">↩</a></li>
<li id="fn:51">Navarro, Jaume (2010). "Electron diffraction chez Thomson: early responses to quantum physics in Britain". The British Journal for the History of Science. 43 (2): 245–275. doi:10.1017/S0007087410000026. ISSN 0007-0874. <a href="https://www.cambridge.org/core/product/identifier/S0007087410000026/type/journal_article" target="_blank">https://www.cambridge.org/core/product/identifier/S0007087410000026/type/journal_article</a> <a href="#fnref:51" class="footnote-back-ref">↩</a></li>
<li id="fn:52">Whittaker, Edmund T. (1989). A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 (Repr ed.). New York: Dover Publ. ISBN 978-0-486-26126-3. <a href="978-0-486-26126-3" target="_blank">978-0-486-26126-3</a> <a href="#fnref:52" class="footnote-back-ref">↩</a></li>
<li id="fn:53">"The Nobel Prize in Physics 1929". The Nobel Foundation. <a href="https://www.nobelprize.org/prizes/physics/1929/summary/" target="_blank">https://www.nobelprize.org/prizes/physics/1929/summary/</a> <a href="#fnref:53" class="footnote-back-ref">↩</a></li>
<li id="fn:54">"The Nobel Prize in Physics 1937". The Nobel Foundation. <a href="https://www.nobelprize.org/prizes/physics/1937/summary/" target="_blank">https://www.nobelprize.org/prizes/physics/1937/summary/</a> <a href="#fnref:54" class="footnote-back-ref">↩</a></li>
<li id="fn:55">Whittaker, Edmund T. (1989). A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 (Repr ed.). New York: Dover Publ. ISBN 978-0-486-26126-3. <a href="978-0-486-26126-3" target="_blank">978-0-486-26126-3</a> <a href="#fnref:55" class="footnote-back-ref">↩</a></li>
<li id="fn:56">Edwards, David A. (1979). "The mathematical foundations of quantum mechanics". Synthese. 42 (1). Springer Science and Business Media LLC: 1–70. doi:10.1007/bf00413704. ISSN 0039-7857. S2CID 46969028. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:56" class="footnote-back-ref">↩</a></li>
<li id="fn:57">Edwards, David A. (1981). "Mathematical foundations of quantum field theory: Fermions, gauge fields, and supersymmetry part I: Lattice field theories". International Journal of Theoretical Physics. 20 (7). Springer Science and Business Media LLC: 503–517. Bibcode:1981IJTP...20..503E. doi:10.1007/bf00669437. ISSN 0020-7748. S2CID 120108219. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:57" class="footnote-back-ref">↩</a></li>
<li id="fn:58">Hanle, P. A. (December 1977), "Erwin Schrodinger's Reaction to Louis de Broglie's Thesis on the Quantum Theory.", Isis, 68 (4): 606–609, doi:10.1086/351880, S2CID 121913205 <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:58" class="footnote-back-ref">↩</a></li>
<li id="fn:59">Pauli, Wolfgang (1926-05-01). "Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik". Zeitschrift für Physik (in German). 36 (5): 336–363. Bibcode:1926ZPhy...36..336P. doi:10.1007/BF01450175. ISSN 0044-3328. S2CID 128132824. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:59" class="footnote-back-ref">↩</a></li>
<li id="fn:60">Mensing, Lucy (1926-11-01). "Die Rotations-Schwingungsbanden nach der Quantenmechanik". Zeitschrift für Physik (in German). 36 (11): 814–823. Bibcode:1926ZPhy...36..814M. doi:10.1007/BF01400216. ISSN 0044-3328. S2CID 123240532. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:60" class="footnote-back-ref">↩</a></li>
<li id="fn:61">Whittaker, Edmund T. (1989). A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 (Repr ed.). New York: Dover Publ. ISBN 978-0-486-26126-3. <a href="978-0-486-26126-3" target="_blank">978-0-486-26126-3</a> <a href="#fnref:61" class="footnote-back-ref">↩</a></li>
<li id="fn:62">Van der Waerden, B. L. (1967). Sources of Quantum Mechanics. Mineola, NY: Dover Publications. pp. 261–76. Received 29 July 1925 See Werner Heisenberg's paper, "Quantum-Theoretical Re-interpretation of Kinematic and Mechanical Relations" pp. 261–76 <a href="#fnref:62" class="footnote-back-ref">↩</a></li>
<li id="fn:63">Busch, Paul; Lahti, Pekka; Werner, Reinhard F. (17 October 2013). "Proof of Heisenberg's Error-Disturbance Relation". Physical Review Letters. 111 (16): 160405. arXiv:1306.1565. Bibcode:2013PhRvL.111p0405B. doi:10.1103/PhysRevLett.111.160405. ISSN 0031-9007. PMID 24182239. S2CID 24507489. <a href="/wiki/Paul_Busch_(physicist)" target="_blank">/wiki/Paul_Busch_(physicist)</a> <a href="#fnref:63" class="footnote-back-ref">↩</a></li>
<li id="fn:64">Appleby, David Marcus (6 May 2016). "Quantum Errors and Disturbances: Response to Busch, Lahti and Werner". Entropy. 18 (5): 174. arXiv:1602.09002. Bibcode:2016Entrp..18..174A. doi:10.3390/e18050174. <a href="https://doi.org/10.3390%2Fe18050174" target="_blank">https://doi.org/10.3390%2Fe18050174</a> <a href="#fnref:64" class="footnote-back-ref">↩</a></li>
<li id="fn:65">Nobel Prize Organization. "Erwin Schrödinger – Biographical". Retrieved 28 March 2014. His great discovery, Schrödinger's wave equation, was made at the end of this epoch-during the first half of 1926. <a href="https://www.nobelprize.org/nobel_prizes/physics/laureates/1933/schrodinger-bio.html" target="_blank">https://www.nobelprize.org/nobel_prizes/physics/laureates/1933/schrodinger-bio.html</a> <a href="#fnref:65" class="footnote-back-ref">↩</a></li>
<li id="fn:66">"Schrodinger Equation (Physics)", Encyclopædia Britannica
 <a href="https://www.britannica.com/EBchecked/topic/528298/Schrodinger-equation" target="_blank">https://www.britannica.com/EBchecked/topic/528298/Schrodinger-equation</a> <a href="#fnref:66" class="footnote-back-ref">↩</a></li>
<li id="fn:67">Erwin Schrödinger, "The Present Situation in Quantum Mechanics", p. 9. "This translation was originally published in Proceedings of the American Philosophical Society, 124, 323–38, and then appeared as Section I.11 of Part I of Quantum Theory and Measurement (J. A. Wheeler and W. H. Zurek, eds., Princeton University Press, NJ 1983). This paper can be downloaded here: Erwin Schrödinger. "A Translation of Schrödinger's "Cat Paradox Paper"". Translated by John D. Trimmer. Archived from the original on 2010-11-13. <a href="https://web.archive.org/web/20101113223658/http://www.tu-harburg.de/rzt/rzt/it/QM/cat.html" target="_blank">https://web.archive.org/web/20101113223658/http://www.tu-harburg.de/rzt/rzt/it/QM/cat.html</a> <a href="#fnref:67" class="footnote-back-ref">↩</a></li>
<li id="fn:68">Heisenberg, W. (1955). The development of the interpretation of the quantum theory, pp. 12–29 in Niels Bohr and the Development of Physics: Essays dedicated to Niels Bohr on the occasion of his seventieth birthday, edited by Pauli, W. with the assistance of Rosenfeld, L. and Weisskopf, V., Pergamon, London, p. 13: "the single quantum jump ... is "factual" in nature". <a href="/wiki/Wolfgang_Pauli" target="_blank">/wiki/Wolfgang_Pauli</a> <a href="#fnref:68" class="footnote-back-ref">↩</a></li>
<li id="fn:69">W. Moore, Schrödinger: Life and Thought, Cambridge University Press (1989), p. 222. See p. 227 for Schrödinger's own words. <a href="#fnref:69" class="footnote-back-ref">↩</a></li>
<li id="fn:70">Gleick, James (21 October 1986). "Physicists finally get to see quantum jump with own eyes". The New York Times. Retrieved 30 November 2019. <a href="https://www.nytimes.com/1986/10/21/science/physicists-finally-get-to-see-quantum-jump-with-own-eyes.html" target="_blank">https://www.nytimes.com/1986/10/21/science/physicists-finally-get-to-see-quantum-jump-with-own-eyes.html</a> <a href="#fnref:70" class="footnote-back-ref">↩</a></li>
<li id="fn:71">Pauling, Linus (1960). The Nature of the Chemical Bond (3rd ed.). Itahca, NY: Cornell University Press. p. 47. ISBN 0801403332. Retrieved 1 March 2016. {{cite book}}: ISBN / Date incompatibility (help) <a href="0801403332" target="_blank">0801403332</a> <a href="#fnref:71" class="footnote-back-ref">↩</a></li>
<li id="fn:72">"Orbital (chemistry and physics)", Encyclopædia Britannica
 <a href="https://www.britannica.com/EBchecked/topic/431159/orbital" target="_blank">https://www.britannica.com/EBchecked/topic/431159/orbital</a> <a href="#fnref:72" class="footnote-back-ref">↩</a></li>
<li id="fn:73">Pauling, Linus (1960). The Nature of the Chemical Bond (3rd ed.). Itahca, NY: Cornell University Press. p. 47. ISBN 0801403332. Retrieved 1 March 2016. {{cite book}}: ISBN / Date incompatibility (help) <a href="0801403332" target="_blank">0801403332</a> <a href="#fnref:73" class="footnote-back-ref">↩</a></li>
<li id="fn:74">Faye, Jan (2019). "Copenhagen Interpretation of Quantum Mechanics". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. <a href="/wiki/Jan_Faye" target="_blank">/wiki/Jan_Faye</a> <a href="#fnref:74" class="footnote-back-ref">↩</a></li>
<li id="fn:75">Camilleri, K.; Schlosshauer, M. (2015). "Niels Bohr as Philosopher of Experiment: Does Decoherence Theory Challenge Bohr's Doctrine of Classical Concepts?". Studies in History and Philosophy of Modern Physics. 49: 73–83. arXiv:1502.06547. Bibcode:2015SHPMP..49...73C. doi:10.1016/j.shpsb.2015.01.005. S2CID 27697360. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:75" class="footnote-back-ref">↩</a></li>
<li id="fn:76">Omnès, Roland (1999). "The Copenhagen Interpretation". Understanding Quantum Mechanics. Princeton University Press. pp. 41–54. doi:10.2307/j.ctv173f2pm.9. S2CID 203390914. <a href="/wiki/Roland_Omn%C3%A8s" target="_blank">/wiki/Roland_Omn%C3%A8s</a> <a href="#fnref:76" class="footnote-back-ref">↩</a></li>
<li id="fn:77">Scheibe, Erhard (1973). The Logical Analysis of Quantum Mechanics. Pergamon Press. ISBN 9780080171586. OCLC 799397091. [T]here is no point in looking for the Copenhagen interpretation as a unified and consistent logical structure. Terms such as "Copenhagen interpretation" or "Copenhagen school" are based on the history of the development of quantum mechanics; they form a simplified and often convenient way of referring to the ideas of a number of physicists who played an important role in the establishment of quantum mechanics, and who were collaborators of Bohr's at his Institute or took part in the discussions during the crucial years. On closer inspection, one sees quite easily that these ideas are divergent in detail and that in particular the views of Bohr, the spiritual leader of the school, form a separate entity which can now be understood only by a thorough study of as many as possible of the relevant publications by Bohr himself. <a href="9780080171586" target="_blank">9780080171586</a> <a href="#fnref:77" class="footnote-back-ref">↩</a></li>
<li id="fn:78">Peres, Asher (2002). "Popper's experiment and the Copenhagen interpretation". Studies in History and Philosophy of Modern Physics. 33: 23. arXiv:quant-ph/9910078. Bibcode:1999quant.ph.10078P. doi:10.1016/S1355-2198(01)00034-X. There seem to be at least as many different Copenhagen interpretations as people who use that term; probably there are more. <a href="/wiki/Asher_Peres" target="_blank">/wiki/Asher_Peres</a> <a href="#fnref:78" class="footnote-back-ref">↩</a></li>
<li id="fn:79">Mermin, N. David (2017-01-01). "Why QBism Is Not the Copenhagen Interpretation and What John Bell Might Have Thought of It". In Bertlmann, Reinhold; Zeilinger, Anton (eds.). Quantum [Un]Speakables II. The Frontiers Collection. Springer International Publishing. pp. 83–93. arXiv:1409.2454. doi:10.1007/978-3-319-38987-5_4. ISBN 9783319389851. S2CID 118458259. <a href="9783319389851" target="_blank">9783319389851</a> <a href="#fnref:79" class="footnote-back-ref">↩</a></li>
<li id="fn:80">Bohr, N. (1928). "The Quantum Postulate and the Recent Development of Atomic Theory". Nature. 121 (3050): 580–590. Bibcode:1928Natur.121..580B. doi:10.1038/121580a0. Available in the collection of Bohr's early writings, Atomic Theory and the Description of Nature (1934). <a href="https://doi.org/10.1038%2F121580a0" target="_blank">https://doi.org/10.1038%2F121580a0</a> <a href="#fnref:80" class="footnote-back-ref">↩</a></li>
<li id="fn:81">Edwards, David A. (1979). "The mathematical foundations of quantum mechanics". Synthese. 42 (1). Springer Science and Business Media LLC: 1–70. doi:10.1007/bf00413704. ISSN 0039-7857. S2CID 46969028. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:81" class="footnote-back-ref">↩</a></li>
<li id="fn:82">Edwards, David A. (1981). "Mathematical foundations of quantum field theory: Fermions, gauge fields, and supersymmetry part I: Lattice field theories". International Journal of Theoretical Physics. 20 (7). Springer Science and Business Media LLC: 503–517. Bibcode:1981IJTP...20..503E. doi:10.1007/bf00669437. ISSN 0020-7748. S2CID 120108219. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:82" class="footnote-back-ref">↩</a></li>
<li id="fn:83">S. Auyang, How is Quantum Field Theory Possible?, Oxford University Press, 1995. <a href="#fnref:83" class="footnote-back-ref">↩</a></li>
<li id="fn:84">The Davisson–Germer experiment, which demonstrates the wave nature of the electron <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger2.html" target="_blank">http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger2.html</a> <a href="#fnref:84" class="footnote-back-ref">↩</a></li>
</ol>

History of quantum mechanics open-in-new

History of quantum mechanics