The Born rule gives the probability of finding a particle in a given quantum state or measurement outcome. For a particle described by a wavefunction, the probability density at a position is the squared magnitude of the wavefunction, written as |ψ|².
German physicist Max Born formulated the rule in 1926 while interpreting solutions to the Schrödinger equation for scattering. The wavefunction itself is generally a complex probability amplitude, not a directly measurable physical density. Squaring its magnitude converts that amplitude into probabilities that can be compared with experimental results.
The rule applies beyond position. It can calculate probabilities for measurements of energy, momentum, angular momentum, and other observables. It also explains why quantum predictions are statistical even when the system’s state is specified precisely. Planck’s law concerns thermal radiation, while Fermi’s golden rule describes transition rates; neither is the general measurement-probability rule.