Wave Function
A complex-valued mathematical function containing all the physical information about the state of an isolated quantum mechanical system.
Governing formula
ψ(x, t) = A e^(i (k x - ω t))
SI unit
m^(-3/2) (in 3D space)
In depth
According to the Born interpretation, the wave function ψ itself is not directly observable, but its squared absolute magnitude |ψ(x,t)|² represents the probability density of finding the particle at position x at time t. Normalization requires the integral of probability density over all space to equal exactly 1.
Examples in the real world
The ground-state 1s wave function of a hydrogen atom describing a spherically symmetric probability cloud around the nucleus.