Born rule

The Born rule was formulated by German physicist Max Born in 1926. In a seminal paper on quantum scattering, Born proposed that the probability of finding a particle at a given location is proportional to the square of the absolute value of its wave function, a postulate that became foundational to the Copenhagen interpretation of quantum mechanics.

The Born rule states that if a quantum system is described by a wave function ψ, the probability of measuring a particular outcome is |ψ|², meaning the square of the wave function's amplitude. For continuous variables like position, this gives a probability density rather than a direct probability, which must be integrated over a region.

The Born rule is generally treated as a fundamental postulate of quantum mechanics rather than something derived from other principles, though numerous attempts have been made to derive it. Approaches such as Gleason's theorem, decision-theoretic derivations within the many-worlds interpretation, and quantum Darwinism have all attempted to provide deeper justification, but none is universally accepted as conclusive.

Max Born received the Nobel Prize in Physics in 1954, notably delayed by nearly three decades after his original contribution. The prize was awarded specifically for his statistical interpretation of the wave function, which is what we now call the Born rule, and he shared it with Walther Bothe.