Psi (Greek)
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Greek alphabet  

Greek alphabet psi.svg  


History  
Use in other languages  
Related topics  
Psi/ˈsaɪ/ (uppercase Ψ, lowercase ψ; Greek: ψι psi [ˈpsi]) 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/ (as in English word "lapse").
For Greek loanwords in Latin and modern languages with Latin alphabets, psi is usually transliterated as "ps".
The letter's origin is uncertain. It may or may not derive 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). In writing, the early letter appears in an angular shape (). There were early graphical variants that omitted the stem ("chickenfootshaped psi" as: or ).
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 "Ѱ".
Use as a symbol
The letter psi is commonly used in physics to represent wave functions in quantum mechanics, such as in 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 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, the division polynomials, and the supergolden ratio
 Water potential in movement of water between plant cells.
 In biochemistry, it denotes the rare nucleotide Pseudouridine.^{[1]}
 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
 Indiana University (as a superimposed I and U)
 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, represents the return value of a program .
 In circadian physiology, ψ represents the phase relationship between a zeitgeber and a biological rhythm.
 In building, to represent an adjustment to a Uvalue, accounting for thermal bridge effects.
 The ordinal collapsing function and notation developed by Wilfried Buchholz^{[2]}
 In Biblical studies, as an abbreviation for the book of Psalms^{[3]}
Character encodings
 Greek / Coptic Psi
Character  Ψ  ψ  ᴪ  Ⲯ  ⲯ  

Unicode name  GREEK CAPITAL LETTER PSI  GREEK SMALL LETTER PSI  GREEK LETTER SMALL CAPITAL PSI  COPTIC CAPITAL LETTER PSI  COPTIC SMALL LETTER PSI  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  936  U+03A8  968  U+03C8  7466  U+1D2A  11438  U+2CAE  11439  U+2CAF 
UTF8  206 168  CE A8  207 136  CF 88  225 180 170  E1 B4 AA  226 178 174  E2 B2 AE  226 178 175  E2 B2 AF 
Numeric character reference  Ψ  Ψ  ψ  ψ  ᴪ  ᴪ  Ⲯ  Ⲯ  ⲯ  ⲯ 
Named character reference  Ψ  ψ  
DOS Greek  150  96  175  AF  
DOS Greek2  212  D4  246  F6  
Windows 1253  216  D8  248  F8  
TeX  \Psi  \psi 
^{ [4] }
 Cyrillic Psi
Character  Ѱ  ѱ  

Unicode name  CYRILLIC CAPITAL LETTER PSI  CYRILLIC SMALL LETTER PSI  
Encodings  decimal  hex  decimal  hex 
Unicode  1136  U+0470  1137  U+0471 
UTF8  209 176  D1 B0  209 177  D1 B1 
Numeric character reference  Ѱ  Ѱ  ѱ  ѱ 
 Mathematical Psi
Character  𝚿  𝛙  𝛹  𝜓  𝜳  𝝍  

Unicode name 
MATHEMATICAL BOLD CAPITAL PSI 
MATHEMATICAL BOLD SMALL PSI 
MATHEMATICAL ITALIC CAPITAL PSI 
MATHEMATICAL ITALIC SMALL PSI 
MATHEMATICAL BOLD ITALIC CAPITAL PSI 
MATHEMATICAL BOLD ITALIC SMALL PSI 

Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120511  U+1D6BF  120537  U+1D6D9  120569  U+1D6F9  120595  U+1D713  120627  U+1D733  120653  U+1D74D 
UTF8  240 157 154 191  F0 9D 9A BF  240 157 155 153  F0 9D 9B 99  240 157 155 185  F0 9D 9B B9  240 157 156 147  F0 9D 9C 93  240 157 156 179  F0 9D 9C B3  240 157 157 141  F0 9D 9D 8D 
UTF16  55349 57023  D835 DEBF  55349 57049  D835 DED9  55349 57081  D835 DEF9  55349 57107  D835 DF13  55349 57139  D835 DF33  55349 57165  D835 DF4D 
Numeric character reference  𝚿  𝚿  𝛙  𝛙  𝛹  𝛹  𝜓  𝜓  𝜳  𝜳  𝝍  𝝍 
Character  𝝭  𝞇  𝞧  𝟁  

Unicode name 
MATHEMATICAL SANSSERIF BOLD CAPITAL PSI 
MATHEMATICAL SANSSERIF BOLD SMALL PSI 
MATHEMATICAL SANSSERIF BOLD ITALIC CAPITAL PSI 
MATHEMATICAL SANSSERIF BOLD ITALIC SMALL PSI 

Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120685  U+1D76D  120711  U+1D787  120743  U+1D7A7  120769  U+1D7C1 
UTF8  240 157 157 173  F0 9D 9D AD  240 157 158 135  F0 9D 9E 87  240 157 158 167  F0 9D 9E A7  240 157 159 129  F0 9D 9F 81 
UTF16  55349 57197  D835 DF6D  55349 57223  D835 DF87  55349 57255  D835 DFA7  55349 57281  D835 DFC1 
Numeric character reference  𝝭  𝝭  𝞇  𝞇  𝞧  𝞧  𝟁  𝟁 
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
Look up Ψ or ψ in Wiktionary, the free dictionary. 
Notes and references
 ^ IUPACIUB Commission on Biochemical Nomenclature (1970). "Abbreviations and symbols for nucleic acids, polynucleotides, and their constituents". Biochemistry. 9 (20): 4022–4027. doi:10.1021/bi00822a023.
 ^ Buchholz, 1986 (Ann. Pure Appl. Logic)
 ^ Gesenius' Hebrew Grammar
 ^ Unicode Code Charts: Greek and Coptic (Range: 037003FF)