Independent electron approximation

<p>In <a href="/facts/Condensed_matter_physics/EBVI5nmL">condensed matter physics</a>, the independent electron approximation is a simplification used in complex systems, consisting of many <a href="/facts/Electrons/L0KBo5cW">electrons</a>, that approximates the electron–electron interaction in crystals as <a href="/facts/Null_(mathematics)/lzWMyRfu">null</a>. It is a requirement for both the <a href="/facts/Free_electron_model/vIyhQHfK">free electron model</a> and the <a href="/facts/Nearly-free_electron_model/fkV4MM5H">nearly-free electron model</a>, where it is used alongside <a href="/facts/Bloch%27s_theorem/oxauccIU">Bloch's theorem</a>. In <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, this approximation is often used to simplify a quantum <a href="/facts/Many-body_problem/n2rIxgwv">many-body problem</a> into single-particle approximations.
</p><p>While this simplification holds for many systems, electron–electron interactions may be very important for certain properties in materials. For example, the theory covering much of <a href="/facts/Superconductivity/pqQAlSzJ">superconductivity</a> is <a href="/facts/BCS_theory/KmlyhxPS">BCS theory</a>, in which the attraction of pairs of electrons to each other, termed "<a href="/facts/Cooper_pair/uHILVyXu">Cooper pairs</a>", is the mechanism behind superconductivity. One major effect of electron–electron interactions is that electrons distribute around the ions so that they <a href="/facts/Screening_effect/hDR3NcJa">screen</a> the ions in the lattice from other electrons.
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Independent electron approximation open-in-new

Independent electron approximation