Psi (letter)
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| [[Image:Greek alphabet {{{letter|alpha-omega}}}.png| 200px|center]] | |
| Greek alphabet | |
|---|---|
| Α α Alpha | Β β Beta |
| Γ γ Gamma | Δ δ Delta |
| Ε ε Epsilon | Ζ ζ Zeta |
| Η η Eta | Θ θ Theta |
| Ι ι Iota | Κ κ Kappa |
| Λ λ Lambda | Μ μ Mu |
| Ν ν Nu | Ξ ξ Xi |
| Ο ο Omicron | Π π Pi |
| Ρ ρ Rho | Σ σ ς Sigma |
| Τ τ Tau | Υ υ Upsilon |
| Φ φ Phi | Χ χ Chi |
| Ψ ψ Psi | Ω ω Omega |
| obsolete letters | |
| Image:Greek alphabet digamma2.png Digamma | Image:Greek alphabet san.png San |
| Image:Greek alphabet qoppa.png Qoppa | Image:Greek alphabet sampi.png Sampi |
| Image:Greek alphabet stigma.png Stigma | Image:Greek alphabet sho.png Sho |
- For other uses, see Psi.
Psi (upper case Ψ, lower case 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 Template:IPA ("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 practise of writing the sigma over the pi, eventually making the combination into a single letter.
It is also used as a symbol/icon for psychology.
Used as a sign for water potential in movement of water between plant cells.
It is perhaps most famous in science for representing a wavefunction in quantum mechanics, particularly with the Schrödinger equation and bra-ket notation (<math>\langle\phi|\psi\rangle</math>)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
- <math> \psi_n(x) = \frac{d^{(n)}}{dx^{(n)}}\frac{\Gamma '(x)}{\Gamma (x)}\,\!</math>
where <math>\Gamma (x)</math> is the gamma function.
Psi was also adopted into the early Cyrillic alphabet. See psi (Cyrillic) (Ѱ, ѱ).
A similar character is used to represent Neptuneals:Ψ ca:Psi da:Psi (bogstav) de:Psi el:Ψι es:Ψ fr:Psi (lettre grecque) gl:Psi ko:Ψ it:Psi (lettera) he:פסי nl:Psi (letter) nds:Psi ja:Ψ pl:Psi (litera) pt:Ψ sv:Psi zh:Ψ