Psi (letter)

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
Obsolete letters
Digamma	Qoppa
San	Sampi
Other characters
Stigma	Sho
Heta

Greek diacritics

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. 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. 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. 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: $\langle\phi|\psi\rangle$ . 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

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

where $\Gamma (x)$ 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).
In mathematics, the number of the "Supergolden Ratio", approximately 1.4 and the solution to the cubic equation x³ = x² + 1.
Water potential in movement of water between plant cells.
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
The Schrodinger Equation and throughout quantum mechanics, ψ(x) stands for the wave function
Indiana University (as a superimposed I and U)
Gangster Disciples
Crips
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 manga Monochrome, Psi is a mentally disturbed character, though her name is usually spelled out.