Psi (letter)

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Greek alphabet
Α α Alpha	Ν ν Nu
Β β Beta	Ξ ξ Xi
Γ γ Gamma	Ο ο Omicron
Δ δ Delta	Π π ϖ Pi
Ε ε Epsilon	Ρ ρ Rho
Ζ ζ Zeta	Σ σ ς Sigma
Η η Eta	Τ τ Tau
Θ θ Theta	Υ υ Upsilon
Ι ι Iota	Φ φ Phi
Κ κ Kappa	Χ χ Chi
Λ λ Lambda	Ψ ψ Psi
Μ μ Mu	Ω ω Omega
Obsolete letters
Ϝ ϝ Digamma	Ϻ ϻ San
Ϙ ϙ Qoppa	Ϡ ϡ Sampi
Ϛ ϛ Stigma	Ϸ ϸ Sho
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. However, in most languages of the world 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 words beginning with the letter in most languages of the world (psychology is pronounced with a silent p for example). The name of the letter is pronounced [saɪ] ("sigh") in English. 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).

The letter psi is commonly used in physics for representing a wavefunction in quantum mechanics, particularly with 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 Γ(x) is the gamma function.

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

• psychology, and sometimes parapsychology (particularly in fiction.).
• water potential in movement of water between plant cells.
• 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
• A Sai, the name of which is pronounced the same way.
• In virology, ψ is a viral packaging signal.