# Psi (letter)

Look up Ψ, ψ in Wiktionary, the free dictionary.
For other uses, see Psi.

Psi (uppercase Ψ, lowercase ψ) 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/ (like in English "lapse"). In Greek, this consonant cluster can occur in the syllable initial position, as in the Greek word "ψάρι" [psári (=fish)]. However, in some languages (including English) this combination is not possible at the beginning of a syllable. In Latin, Greek words beginning with psi are transcribed by ps-, but seem to have been pronounced simply as s-, with a quiescent p.[citation needed] This pronunciation has affected that of Greek loanwords beginning with the letter in several languages. In English, for example, psychology is pronounced with a silent p, and the name of the letter is often pronounced [saɪ] ("sigh"), although this is not always the case. Any person who has learned Greek is aware that the correct pronunciation is actually "p'see".[citation needed] The letter was adopted into the Old Italic alphabet, and its shape is continued into the Algiz rune of the Elder Futhark.

The letter may have originated from the practice of writing the sigma over the pi, eventually making the combination into a single letter.[citation needed] Psi was also adopted into the early Cyrillic alphabet. See psi (Cyrillic) (Ѱ, ѱ). This may have also been since the letter, both in lower case and uppercase form, resembles the trident wielded by Poseidon, the Greek god of water/ocean.

The letter psi is commonly used in physics for representing a wavefunction in quantum mechanics, particularly with the Schrödinger equation and bra-ket notation: ${\displaystyle \langle \phi |\psi \rangle }$. 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

${\displaystyle \psi _{n}(x)={\frac {d^{(n)}}{dx^{(n)}}}{\frac {\Gamma '(x)}{\Gamma (x)}}\,\!}$

where ${\displaystyle \Gamma (x)}$ is the gamma function.

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