Psi

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

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.