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Psi (Greek)

Penultimate letter in the Greek alphabet

Psi (Ψ, ψ, 𝛙; Greek: ψι psi) is the twenty-third letter of the Greek alphabet with a numeric value of 700, representing the /ps/ sound in both Classical and Modern Greek. Its origins may trace back to the Phoenician alphabet, appearing in the 7th century BC with different regional sounds, including /kʰ/ in the Western alphabets. Psi influenced the Old Italic alphabets and the Elder Futhark rune Algiz (ᛉ). It was briefly used as "Antisigma" during Emperor Claudius's reign (Claudian letters) and later adopted into the early Cyrillic alphabet as Ѱ.

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Use as a symbol

The symbol Ψ or ψ has many uses across different academic and informal contexts:

Wave functions in quantum mechanics
The generalized positional states of a qubit in a quantum computer
The polygamma function ³

The fields of psychology, psychiatry, and sometimes parapsychology ⁴
The reciprocal Fibonacci constant,⁵ the division polynomials, and the supergolden ratio
The second Chebyshev function ⁶
Water potential in movement of water between plant cells⁷
In biochemistry, it denotes pseudouridine, an uncommon nucleoside ⁸
A stream function in fluid mechanics
One of the dihedral angles in the backbones of proteins ⁹
Indiana University (as a superimposed I and U)¹⁰
A sai, whose name is pronounced the same way in English
Pharmacology, general pharmacy
The retroviral psi packaging element ¹¹
The J/psi meson in particle physics ¹²
The return value of a program in computability theory
The phase relationship between a zeitgeber and a biological rhythm ¹³
In building, to represent an adjustment to a U-value, accounting for thermal bridge effects
The ordinal collapsing function and notation ¹⁴
In Biblical studies, as an abbreviation for the book of Psalms ¹⁵

Unicode

U+03A8 Ψ GREEK CAPITAL LETTER PSI (Ψ)¹⁶
U+03C8 ψ GREEK SMALL LETTER PSI (ψ)
U+0470 Ѱ CYRILLIC CAPITAL LETTER PSI
U+0471 ѱ CYRILLIC SMALL LETTER PSI
U+1D2A ᴪ GREEK LETTER SMALL CAPITAL PSI
U+2CAE Ⲯ COPTIC CAPITAL LETTER PSI
U+2CAF ⲯ COPTIC SMALL LETTER PSI
U+1D6BF 𝚿 MATHEMATICAL BOLD CAPITAL PSI¹⁷
U+1D6D9 𝛙 MATHEMATICAL BOLD SMALL PSI
U+1D6F9 𝛹 MATHEMATICAL ITALIC CAPITAL PSI
U+1D713 𝜓 MATHEMATICAL ITALIC SMALL PSI
U+1D733 𝜳 MATHEMATICAL BOLD ITALIC CAPITAL PSI
U+1D74D 𝝍 MATHEMATICAL BOLD ITALIC SMALL PSI
U+1D76D 𝝭 MATHEMATICAL SANS-SERIF BOLD CAPITAL PSI
U+1D787 𝞇 MATHEMATICAL SANS-SERIF BOLD SMALL PSI
U+1D7A7 𝞧 MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL PSI
U+1D7C1 𝟁 MATHEMATICAL SANS-SERIF BOLD ITALIC SMALL PSI

Notes and references

References

"psi". The Chambers Dictionary (9th ed.). Chambers. 2003. ISBN 0-550-10105-5. 0-550-10105-5 ↩
Oliver, Revilo P. (1949). "The Claudian Letter Ⱶ". American Journal of Archaeology. 53 (3): 249–257. doi:10.2307/500662. JSTOR 500662. S2CID 193082268. /wiki/Doi_(identifier) ↩
Weisstein, Eric W. "Polygamma Function". mathworld.wolfram.com. Retrieved 2025-02-08. A special function mostly commonly denoted ψ_n(z), ψ^((n))(z), or F_n(z-1)... https://mathworld.wolfram.com/PolygammaFunction.html ↩
"About - The Parapsychological Association". www.parapsych.org. Retrieved 2025-02-09. The Parapsychological Association, Inc. (PA) is the international professional organization of scientists and scholars engaged in the study of 'psi' (or 'psychic') experiences, such as telepathy, clairvoyance, remote viewing, psychokinesis, psychic healing, and precognition. https://www.parapsych.org/base/about.aspx ↩
Weisstein, Eric W. "Reciprocal Fibonacci Constant". mathworld.wolfram.com. Retrieved 2025-02-01. https://mathworld.wolfram.com/ReciprocalFibonacciConstant.html ↩
Weisstein, Eric W. "Chebyshev Functions". mathworld.wolfram.com. Retrieved 2025-02-01. https://mathworld.wolfram.com/ChebyshevFunctions.html ↩
WELBAUM, GREGORY E.; BRADFORD, KENT J. (1991-03-01). "Water Relations of Seed Development and Germination in Muskmelon (Cucumis melo L.): VI. INFLUENCE OF PRIMING ON GERMINATION RESPONSES TO TEMPERATURE AND WATER POTENTIAL DURING SEED DEVELOPMENT". Journal of Experimental Botany. 42 (3): 393–399. doi:10.1093/jxb/42.3.393. ISSN 0022-0957. Germination sensitivities to temperature and water potential (ψ) were quantified as indicators of the influence of seed maturity and priming on seed vigour. https://academic.oup.com/jxb/article-abstract/42/3/393/495356?redirectedFrom=fulltext ↩
IUPAC-IUB Commission on Biochemical Nomenclature (1970). "Abbreviations and symbols for nucleic acids, polynucleotides, and their constituents". Biochemistry. 9 (20): 4022–4027. doi:10.1021/bi00822a023. /wiki/Biochemistry_(journal) ↩
"Torsion Angles and the Ramachnadran Plot in Protein Structures". proteinstructures.com. Retrieved 2025-02-09. These angles describe the rotations of the polypeptide backbone around the bonds between N-Cα (called Phi, φ) and Cα-C (called Psi, ψ) and essentially determine the fold of the protein. https://proteinstructures.com/structure/ramachandran-plot/ ↩
Although the university itself refers to its logo as a trident, not the Greek letter psi: "The IU trident—the only logo at Indiana University". Indiana University. Retrieved 2020-07-31. At IU, the trident is the only logo we use, both institution-wide and at the unit level. /wiki/Trident ↩
Rein, Alan (2020-07-28). "The heart of the HIV RNA packaging signal?". Proceedings of the National Academy of Sciences of the United States of America. 117 (33). doi:10.1073/pna. Archived from the original on 2025-01-03. vRNA is selectively packaged because it contains a "packaging signal" or "ψ" [also designated the "core encapsidation signal" (2)]. http://web.archive.org/web/20250103000531/https://pmc.ncbi.nlm.nih.gov/articles/PMC7443930/ ↩
"J/psi particle | Quark, Charm & Meson | Britannica". www.britannica.com. Retrieved 2025-02-09. J/psi particle, type of meson consisting of a charmed quark and a charmed antiquark. https://www.britannica.com/science/J-psi-particle ↩
Srivastava, Manishi; Varma, Vishwanath; Abhilash, Lakshman; Sharma, Vijay Kumar; Sheeba, Vasu (June 2019). "Circadian Clock Properties and Their Relationships as a Function of Free-Running Period in Drosophila melanogaster". Journal of Biological Rhythms. 34 (3): 231–248. doi:10.1177/0748730419837767. ISSN 1552-4531. PMID 30939971. ... 2) accuracy (i.e., day-to-day stability of the phase relationship (ψ), where ψ is the duration between a phase of the rhythm and a phase of the external cycle) is greater for clocks with τ close to 24 h; ... https://pubmed.ncbi.nlm.nih.gov/30939971/ ↩
Buchholz, W. (1986). "A new System of proof-theoretic ordinal functions" (PDF). Ann. Pure Appl. Logic. 32 (3): 195–207. doi:10.1016/0168-0072(86)90052-7. https://epub.ub.uni-muenchen.de/3841/1/3841.pdf ↩
Gesenius' Hebrew Grammar https://en.wikisource.org/wiki/Template:GHGbible-ref ↩
Unicode Code Charts: Greek and Coptic (Range: 0370-03FF) https://www.unicode.org/charts/PDF/U0370.pdf ↩
The MATHEMATICAL characters are used in math. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style. ↩

Use as a symbol

Unicode

See also

Notes and references

References