Psi (letter)

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Template:Pp-semi-indef

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Psi uc lc.svg
Greek alphabet
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
  • Digamma
  • Heta
  • San
  • Koppa
  • Sampi
  • Tsan
Numerals
ϛ (6)
ϟ (90)
ϡ (900)
In other languages
Scientific symbols

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The Greek alphabet on a black-figure pottery vessel, with an archaic chickenfoot-shaped psi.

Psi (uppercase Ψ{{#invoke:Category handler|main}}, lowercase ψ{{#invoke:Category handler|main}}; Greek: Ψι{{#invoke:Category handler|main}} Psi) 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". In English, the letter is pronounced Template:IPAc-en or sometimes Template:IPAc-en. (In Greek, it is pronounced Template:IPA-el.)

The letter is a Greek innovation and not derived from the Phoenician alphabet. Template:Fact 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".

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: . 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

where is the gamma function.

The letters Ψ or ψ can also be a symbol for:

Character Encodings

  • Greek / Coptic Psi

Template:Charmap [2]

  • Cyrillic Psi

Template:Charmap

  • Mathematical Psi

Template:Charmap

Template:Charmap

These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

See also

Notes and references

  1. Buchholz, 1986 (Ann. Pure Appl. Logic)
  2. Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)