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{{Wiktionary|Ψ|ψ}}
{{Greek Alphabet|letter=psi|image=Greek alphabet psi.svg}}
[[File:NAMA Alphabet grec.jpg|thumb|The Greek alphabet on a [[black-figure pottery]] vessel, with an archaic chickenfoot-shaped psi.]]
 
'''Psi''' (uppercase '''{{lang|el|Ψ}}''', lowercase '''{{lang|el|ψ}}'''; {{Lang-el|Ψι}} ''Psi'') 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/ (as in English word "lapse").
 
For Greek loanwords in Latin and modern languages with Latin alphabets, psi is usually transliterated as "ps".  In English, the letter is pronounced {{IPAc-en|ˈ|s|aɪ}} or sometimes {{IPAc-en|ˈ|p|s|aɪ}}. (In Greek, it was pronounced {{IPA-el|ˈpsiː|}}.)
 
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 Greek alphabet|Western alphabets]] (the sound  expressed by [[Χ]] in the Eastern alphabets). In writing, the early letter appears in an angular shape ([[File:Greek Psi straight.svg|15px|]]).
There were early graphical variants that omitted the stem ("chickenfoot-shaped psi" as: [[File:Greek Psi V-shaped.svg|15px]] or [[File:Greek Chi 05.svg|15px]]).
 
The Western letter (expressing  /kʰ/, 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 "[[psi (Cyrillic)|{{Unicode|Ѱ}}]]".
 
==Use as a symbol==
The letter psi is commonly used in [[physics]] to represent [[wavefunctions]] in [[quantum mechanics]], such as in 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^{(m)}(z) = \frac{d^m}{dz^m} \frac{\Gamma' (z)}{\Gamma (z)}</math>
where <math>\Gamma (z)</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, 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]] [[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]]
*[[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 [[computability theory]], <math> \psi_P(x)\,\!</math> represents the return value <math> Y\,\!</math> of a program <math> P\,\!</math>.
*In [[circadian physiology]], ψ represents the phase relationship between a [[zeitgeber]] and a [[biological rhythm]].
 
==Character Encodings==
 
* Greek / Coptic Psi
 
{{charmap
|03A8|name1=Greek Capital Letter Psi
|03C8|name2=Greek Small Letter Psi
|1D2A|name3=Greek Letter Small Capital Psi
|2CAE|name4=Coptic Capital Letter Psi
|2CAF|name5=Coptic Small Letter Psi
|map2=DOS Greek|map2char1=96|map2char2=AF
|map3=DOS Greek-2|map3char1=D4|map3char2=F6
|map4=Windows 1253|map4char1=D8|map4char2=F8
|namedref1=[[TeX]]|ref1char1=\Psi|ref1char2=\psi
}}
<ref>Unicode Code Charts: [http://www.unicode.org/charts/PDF/U0370.pdf Greek and Coptic (Range: 0370-03FF)]</ref>
 
* Cyrillic Psi
 
{{charmap
|0470|name1=Cyrillic Capital Letter Psi
|0471|name2=Cyrillic Small Letter Psi
}}
 
* Mathematical Psi
 
{{charmap
|1D6BF|name1=Mathematical Bold<br />Capital Psi
|1D6D9|name2=Mathematical Bold<br />Small Psi
|1D6F9|name3=Mathematical Italic<br />Capital Psi
|1D713|name4=Mathematical Italic<br />Small Psi
|1D733|name5=Mathematical Bold Italic<br />Capital Psi
|1D74D|name6=Mathematical Bold Italic<br />Small Psi
}}
 
{{charmap
|1D76D|name1=Mathematical Sans-Serif<br />Bold Capital Psi
|1D787|name2=Mathematical Sans-Serif<br />Bold Small Psi
|1D7A7|name3=Mathematical Sans-Serif<br />Bold Italic Capital Psi
|1D7C1|name4=Mathematical Sans-Serif<br />Bold Italic Small Psi
}}
 
These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.
 
==See also==
*[[Psi and phi type figurine]]
*[[Psi (Cyrillic)]]
 
== Notes and references ==
<references/>
 
{{DEFAULTSORT:Psi (Letter)}}
[[Category:Greek letters]]

Latest revision as of 21:25, 9 March 2014

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