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https://en.wikipedia.org/wiki/Psi_(Greek)
Psi (Greek)
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This article is about the Greek letter. For the Cyrillic letter, see Psi (Cyrillic).
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Psi uc lc.svg
Greek alphabet
Greek alphabet psi.svg
Αα Alpha Νν Nu
Ββ Beta Ξξ Xi
Γγ Gamma Οο Omicron
Δδ Delta Ππ Pi
Εε Epsilon Ρρ Rho
Ζζ Zeta Σσς Sigma
Ηη Eta Ττ Tau
Θθ Theta Υυ Upsilon
Ιι Iota Φφ Phi
Κκ Kappa Χχ Chi
Λλ Lambda Ψψ Psi
Μμ Mu Ωω Omega
History
Archaic local variants
DigammaHetaSanKoppaSampiTsan
DiacriticsLigatures
Numerals
ϛ (6)ϟ (90)ϡ (900)
Use in other languages
BactrianCopticAlbanian
Related topics
Use as scientific symbols
Wikipedia book BookCategory Category
Commons page Commons
vte
The Greek alphabet on a black-figure pottery vessel, with an archaic chickenfoot-shaped psi.
Psi /ˈsaɪ/ (uppercase Ψ, lowercase ψ; Greek: ψι psi [ˈpsi]) is the 23rd letter of the Greek alphabet and has a numeric value of 700. In both Classical and Modern Greek, the letter indicates the combination /ps/ (as in English word "lapse").
For Greek loanwords in Latin and modern languages with Latin alphabets, psi is usually transliterated as "ps".
The letter's origin is uncertain. It may or may not derive from the Phoenician alphabet. It appears in the 7th century BC, expressing /ps/ in the Eastern alphabets, but /kʰ/ in the Western alphabets (the sound expressed by Χ in the Eastern alphabets). In writing, the early letter appears in an angular shape (Greek Psi straight.svg). There were early graphical variants that omitted the stem ("chickenfoot-shaped psi" as: Greek Psi V-shaped.svg or Greek Chi 05.svg).
The Western letter (expressing /kʰ/, later /x/) was adopted into the Old Italic alphabets, and its shape is also continued into the Algiz rune of the Elder Futhark. The classical Greek letter was adopted into the early Cyrillic alphabet as "Ѱ".
Contents
1 Use as a symbol
2 Character encodings
3 See also
4 Notes and references
Use as a symbol
The letter psi is commonly used in physics to represent wave functions in quantum mechanics, such as in the Schrödinger equation and bra–ket notation: {\displaystyle \langle \phi |\psi \rangle }\langle \phi |\psi \rangle . It is also used to represent the (generalized) positional states of a qubit in a quantum computer.
Psi is also used as the symbol for the polygamma function, defined by
{\displaystyle \psi ^{(m)}(z)={\frac {d^{m}}{dz^{m}}}{\frac {\Gamma '(z)}{\Gamma (z)}}}\psi ^{(m)}(z)={\frac {d^{m}}{dz^{m}}}{\frac {\Gamma '(z)}{\Gamma (z)}}
where {\displaystyle \Gamma (z)}\Gamma (z) is the gamma function.
The letters Ψ or ψ can also be a symbol for:
psychology, psychiatry, and sometimes parapsychology (involving paranormal or relating with the supernatural subjects, especially research into extrasensory perception).
In mathematics, the reciprocal Fibonacci constant, the division polynomials, and the supergolden ratio
Water potential in movement of water between plant cells.
In biochemistry, it denotes the rare nucleotide Pseudouridine.[1]
Stream function in fluid mechanics defining the curve to which the flow velocity is always tangent.
One of the dihedral angles in the backbones of proteins
The planet Neptune
Indiana University (as a superimposed I and U)
A sai, the name of which is pronounced the same way.
Pharmacology, general pharmacy
In virology the ψ site is a viral packaging signal.
The J/ψ meson, in particle physics.
In the computability theory, {\displaystyle \psi {P}(x)\,!}\psi {P}(x)\,! represents the return value {\displaystyle Y\,!}Y\,! of a program {\displaystyle P\,!}P\,!.
In circadian physiology, ψ represents the phase relationship between a zeitgeber and a biological rhythm.
In building, to represent an adjustment to a U-value, accounting for thermal bridge effects.
The ordinal collapsing function and notation developed by Wilfried Buchholz[2]
In Biblical studies, as an abbreviation for the book of Psalms[3]