The Born rule, also known as the Born interpretation or Born's probability rule, is a fundamental principle in quantum mechanics that describes how to calculate probabilities of outcomes in quantum measurements. It was formulated by the physicist Max Born in 1926.
According to the Born rule, the probability of obtaining a particular measurement outcome in a quantum system is proportional to the square of the absolute value of the complex probability amplitude associated with that outcome. Mathematically, for a quantum state represented by a wavefunction ψ, the probability P of obtaining a particular outcome associated with an observable is given by:
P = |ψ|^2,
where |ψ|^2 represents the squared magnitude of the probability amplitude.
The Born rule provides a way to connect the mathematical formalism of quantum mechanics, described by wavefunctions or state vectors, to observable quantities that can be measured. It allows predictions to be made about the probabilities of different outcomes when a measurement is performed on a quantum system.
It is worth noting that the Born rule deals with the statistical interpretation of quantum mechanics, where the outcomes of individual measurements are inherently probabilistic. The precise outcome of a measurement cannot be predicted with certainty in many cases but rather determined by the probabilities associated with different measurement results. The Born rule provides a key tool for calculating and understanding these probabilities within the framework of quantum mechanics.