A lowercase Greek letter commonly used to represent wave functions in quantum mechanics and potential functions in physics.
Examples
Wave function in quantum mechanics
\psi(x,t) = A\cos(kx - \omega t)
Characteristic function in probability theory
\psi_X(t) = \mathbb{E}[e^{itX}] = \int_{-\infty}^{\infty} e^{itx}f_X(x)dx
General function notation in mathematics
\psi: G \rightarrow H \text{ is a homomorphism}