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
Other characters
	Digamma		Stigma
	Heta		San
	Qoppa		Sampi
Greek diacritics

For other uses, see Psi.

Psi (uppercase Ψ, lowercase ψ; pronounced in English as /ˈsaɪ/, sigh) 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"). The letter was adopted into the Old Italic alphabet, and its shape is continued into the Algiz rune of the Elder Futhark. Psi was also adopted into the early Cyrillic alphabet as Ѱ. In Greek loanwords in Latin and modern languages with Latin alphabets, Psi is usually transliterated as "ps". In English, due to phonotactic constraints, its pronunciation is usually simplified to /s/.

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 reciprocal Fibonacci constant.
Water potential in movement of water between plant cells.
In biochemistry, it denotes the rare nucleotide pseudouridilic acid.
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 Schrödinger equation and throughout quantum mechanics, ψ(x) stands for the wave function
Indiana University (as a superimposed I and U)
Gangster Disciples
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, $\psi_P(x)\,\!$ represents the return value $Y\,\!$ of a program $P\,\!$ .
In the comic Monochrome, Psi is a mentally disturbed character, though her name is usually spelled out.
In the television show Babylon 5, Ψ is the symbol of the Psi Corps.
On Wikipedia, it stands for the currency WikiMoney, an inactive mutual funds system.

Psi (letter)

See also