Psi (uppercase Ψ, lowercase ψ or 𝛙; psi ) is the twenty-third and penultimate letter of the Greek alphabet and is associated with a numeric value of 700. In both Classical and Modern Greek, the letter indicates the combination (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 in the Eastern alphabets, but in the Western alphabets (the sound expressed by Χ in the Eastern alphabets). In writing, the early letter appears in an angular shape. There were early graphical variants that omitted the stem ("chickenfoot-shaped psi" as: or ). The Western letter (expressing, later ) was adopted into the Old Italic alphabets, and its shape is also continued into the Algiz rune <ᛉ> of the Elder Futhark. Psi, or its Arcadian variant or was adopted in the Latin alphabet in the form of "Antisigma" (Ↄ, ↃC, or 𐌟) during the reign of Emperor Claudius as one of the three Claudian letters. However, it was abandoned after his death. 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 \Gamma (z) is the gamma function. The letters Ψ or ψ can also be a symbol for:

Unicode

Notes and references