Born rule

The Born rule (also called the Born law, Born's rule, or Born's law) formulated by German physicist Max Born in 1926, is a law of quantum mechanics giving the probability that a measurement on a quantum system will yield a given result. In its simplest form it states that the square of the magnitude of the wavefunction of a particle gives the probability of finding the particle at each point. The Born rule is one of the key principles of quantum mechanics. There have been many attempts to derive the Born rule from the other assumptions of quantum mechanics, with inconclusive results.

The Born rule states that if an observable corresponding to a Hermitian operator ${\displaystyle A}$ with discrete spectrum is measured in a system with normalized wave function ${\displaystyle |\psi \rangle }$ (see bra–ket notation), then

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