A wave function is defined to be a function describing the probability of a particle's quantum state as a function of position, momentum, time, and/or spin. Wave functions are commonly denoted by the variable Ψ.

A wave function may be used to describe the probability of finding an electron within a matter wave. To do this, the wave function, which may include an imaginary number, is squared to yield a real number solution. Then, the probability of an electron being within a certain area can be assessed.

The famous Schrodinger equation introduced the concept of a wave function in 1925.