Psi
Psi (Ψ, ψ) is the 23rd letter of the Greek alphabet, said “sye” or “psye”. In quantum physics Ψ and ψ are the wave function in the Schrödinger equation.
Easily confused with
How to read it
Dictionary.com gives the American pronunciation as “sye” or “psye”; the Cambridge Dictionary gives British /psaɪ/ or /saɪ/ and American /saɪ/. Collins describes psi as a composite consonant, transliterated as ps. The same letters, psi, are also the abbreviation for pounds per square inch, a unit of pressure (Dictionary.com), as in the maximum pressure moulded on a tire sidewall, and a word for purported psychic phenomena.
Also searched as: psi letter, psi symbol, ψ, Ψ, ψ meaning.
Capital and small forms
| Form | Character | Code point | Unicode name |
|---|---|---|---|
| Capital | Ψ | U+03A8 | GREEK CAPITAL LETTER PSI |
| Small | ψ | U+03C8 | GREEK SMALL LETTER PSI |
In quantum physics
The wave function of a particle is written with psi. OpenStax’s University Physics uses “big psi” Ψ(x, t) for the time-dependent wave function and “little psi” ψ(x) for the time-independent one. The probability of finding the particle between x and x + dx is |Ψ(x, t)|² dx. The time-dependent Schrödinger equation is −(ħ²/2m) ∂²Ψ/∂x² + UΨ = iħ ∂Ψ/∂t.
The ħ in it is not a Greek letter. It is the reduced Planck constant, Planck’s constant divided by 2π: Unicode names the character ℏ (U+210F) “PLANCK CONSTANT OVER TWO PI”, and CODATA 2022 gives it as exactly 1.054 571 817… × 10⁻³⁴ J s (NIST). In Bra-ket notation (|ψ⟩) a quantum state is written |ψ⟩.
Psi in maths and particle physics
In maths ψ(z) is the psi or digamma function, ψ(z) = Γ′(z)/Γ(z), the derivative of the Gamma function divided by the function itself (NIST DLMF §5.2). In particle physics ψ is part of the name of the J/ψ meson, which OpenStax lists at 3100 MeV.
Where this symbol came from
oldsymbols.comSchrödinger’s catSchrödinger’s cat is a thought experiment the physicist Erwin Schrödinger published in 1935: a cat shut in a steel chamber that quantum mechanics, taken literally, would describe as alive and dead at once until someone looks. He offered it as a ridiculous case, to question the theory; it has since become a popular emblem for anything undecided.Write in Greek letters
stringmash.comGreek alphabet translatorWrite English in Greek letters by sound, or turn Greek back into Latin letters as Greek passports do.Read next
- Next in Greek lettersOmegaOmega (Ω, ω) is the 24th and last letter of the Greek alphabet. The capital Ω is the symbol for the ohm, the SI unit of electrical resistance, and the small ω is angular frequency in physics.
- In Physics and chemistry symbolsh-bar (ħ)ħ, said “h-bar”, is the reduced Planck constant: the Planck constant h divided by 2π. Its value is exactly 1.054 571 817… × 10⁻³⁴ joule seconds, and it appears in the basic equations of quantum physics.
More greek letters
The same shape elsewhere
Browse symbols drawn with letters and numbers.
Sources
- psi (Dictionary.com entry), Dictionary.com Unabridged; Collins English Dictionary, Dictionary.com, Entry, American and British (Collins) senses
- psi (Cambridge Dictionary entry), Cambridge Advanced Learner’s Dictionary, Cambridge University Press, Entry
- Greek and Coptic: Range 0370–03FF (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Greek capital and small letters
- University Physics Volume 3, 7.3 The Schrödinger Equation, OpenStax (Rice University), Section 7.3
- University Physics Volume 3, 7.1 Wave Functions, OpenStax (Rice University), Section 7.1
- Letterlike Symbols: Range 2100–214F (code chart), The Unicode Standard, Version 18.0, Unicode Consortium, Letterlike symbols
- CODATA Value: reduced Planck constant, 2022 CODATA recommended values, National Institute of Standards and Technology, Value
- NIST Digital Library of Mathematical Functions, §5.2 Gamma and Psi Functions, U.S. National Institute of Standards and Technology, §5.2(i)
- University Physics Volume 3, 11.1 Introduction to Particle Physics, OpenStax (Rice University), Table 11.1
Researched, edited and approved by Rory Hansen before publishing. Last reviewed September 30, 2026. How we research
Added .