Wave function

Summary

A wave function is a pure quantum state written as a complex-valued square-integrable function, usually of the positions of the particles. For one particle in $\R^n$, it is a function $\psi$ in $L^2(\R^n)$ with $\int \abs{\psi}^2 = 1$, and $\abs{\psi(x)}^2$ is the probability density of the position. Its time evolution is given by the Schrödinger equation. Two wave functions that differ by a constant factor of modulus $1$ describe the same state.