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*psi (letter)*

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psi (letter)

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**Psi**({{IPAc-en|(|p|)|s|aÉª}}; uppercase

**';**

*', lowercase**psi*{{IPA-el|Ëˆpsi|}}) 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 /kÊ°/ in the Western alphabets (the sound expressed by Î§ 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 /kÊ°/, 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 "Ñ°".

## Use as a symbol

The letter psi is commonly used in physics to represent wave functions in quantum mechanics, such as in the SchrÃ¶dinger equation and braâ€“ket notation: langlephi|psirangle. 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
psi^{(m)}(z) = frac{d^m}{dz^m} frac{Gamma' (z)}{Gamma (z)}

where Gamma (z) is the gamma function.The letters Î¨ or Ïˆ 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.JOURNAL, IUPAC-IUB Commission on Biochemical Nomenclature, 10.1021/bi00822a023, Abbreviations and symbols for nucleic acids, polynucleotides, and their constituents, Biochemistry (journal), Biochemistry, 9, 20, 4022â€“4027, 1970, 5499957, 1179624,
- 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 Ïˆ site is a viral packaging signal.
- The J/Ïˆ meson, in particle physics.
- In the computability theory, psi_P(x),! represents the return value Y,! of a program P,!.
- In circadian physiology, Ïˆ represents the phase relationship between a zeitgeber and a biological rhythm.
- In building, to represent an adjustment to a U-value, accounting for thermal bridge effects.
- The ordinal collapsing function and notation developed by Wilfried BuchholzBuchholz, 1986 (Ann. Pure Appl. Logic)

## Character encodings

- Greek / Coptic Psi

name1=Greek Capital Letter Psi | name2=Greek Small Letter Psi | name3=Greek Letter Small Capital Psi | name4=Coptic Capital Letter Psi | name5=Coptic Small Letter Psi | map2char1=96|map2char2=AF | map3char1=D4|map3char2=F6 | map4char1=D8|map4char2=F8 | TeX>ref1char1=Psi|ref1char2=psi}}Unicode Code Charts: Greek and Coptic (Range: 0370-03FF) - Cyrillic Psi
| name1=Cyrillic Capital Letter Psi | name2=Cyrillic Small Letter Psi}} - Mathematical Psi
| name1=Mathematical BoldCapital Psi | name2=Mathematical BoldSmall Psi | name3=Mathematical ItalicCapital Psi | name4=Mathematical ItalicSmall Psi | name5=Mathematical Bold ItalicCapital Psi | name6=Mathematical Bold ItalicSmall Psi}}{{charmap | name1=Mathematical Sans-SerifBold Capital Psi | name2=Mathematical Sans-SerifBold Small Psi | name3=Mathematical Sans-SerifBold Italic Capital Psi | name4=Mathematical Sans-SerifBold 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{{Wiktionary|Î¨|Ïˆ}}## Notes and references |

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