Psi (Greek)

Psi (/ˈpsaɪ/ or /ˈsaɪ/; uppercase Ψ, lowercase ψ; after Greek ψῖ /ˈpsiː/) 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 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/ at the beginning of a word.

Historically, the letter is a Greek innovation and not derived from the Phoenician alphabet. 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). Epigraphically, the early letter appears in an angular shape (). There were early graphical variants which omitted the stem ("chickenfoot-shaped psi" ).

The Western letter (expressing /kʰ/, and 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 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, especially research into extrasensory perception).
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 television show Babylon 5, Ψ is the symbol of the Psi Corps.
In circadian physiology, ψ represents the phase relationship between a zeitgeber and a biological rhythm.

Notes and references

Use as a symbol

See also

Notes and references