Psi
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| - | Ψ ψ Psi | + | '''Psi''' (uppercase '''Ψ''', lowercase '''ψ'''; pronounced in English as ''sigh'') is the 23rd letter of the [[Greek alphabet]] and has a [[Greek numerals|numeric]] value of 700. In both [[Classical Greek|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 [[psi (Cyrillic)|Ѱ]]. In Greek loanwords in Latin and modern languages with Latin alphabets, Psi is usually transliterated as "ps". In English, due to [[English phonology#Phonotactics|phonotactic constraints]], its pronunciation is usually simplified to /s/. |
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| + | The letter psi is commonly used in [[physics]] for representing a [[wavefunction]] in [[quantum mechanics]], particularly with the [[Schrödinger equation]] and [[bra-ket notation]]: <math>\langle\phi|\psi\rangle</math>. It is also used to represent the (generalized) positional states of a [[qubit]] in a [[quantum computer]]. | ||
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| + | 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]]. | ||
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| + | 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]] [[Pseudouridine|pseudouridilic acid]]. | ||
| + | *[[Stream function]] in [[fluid mechanics]] defining the curve to which the [[flow velocity]] is always [[tangent]]. | ||
| + | *One of the [[dihedral angle]]s 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 (weapon)|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 comic [[Monochrome]], Psi is a mentally disturbed character, though her name is usually spelled out. | ||
| + | *In the television show [http://babylon5.warnerbros.com/ Babylon 5], Ψ is the symbol of the [[Psi Corps|Psi Corps]]. | ||
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| + | ==See also== | ||
| + | *[[Psi and phi type figurine]] | ||
| + | *[[Psi (Cyrillic)]] | ||
| + | [[Category:Greek letters]] | ||
Revision as of 08:19, 16 January 2010
Psi (uppercase Ψ, lowercase ψ; pronounced in English as 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: <math>\langle\phi|\psi\rangle</math>. 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
- <math> \psi_n(x) = \frac{d^{(n)}}{dx^{(n)}}\frac{\Gamma '(x)}{\Gamma (x)}\,\!</math>
where <math>\Gamma (x)</math> 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 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.
