The Born rule is a fundamental principle in quantum mechanics that relates the mathematical description of a quantum system to the probabilities of measuring different outcomes when the system is observed. It is named after the German physicist Max Born, who first formulated the rule in 1926.
The Born rule states that the probability of obtaining a particular measurement outcome in a quantum system is proportional to the squared magnitude of the wave function describing the system at the time of measurement. Mathematically, this is expressed as:
P(a) = |ψ(a)|^2
where P(a) is the probability of measuring outcome “a”, and ψ(a) is the component of the wave function that corresponds to outcome “a”. The sum of the probabilities of all possible outcomes must be equal to 1, which reflects the fact that the system must be in some definite state when it is observed.
The Born rule is a fundamental principle of quantum mechanics and has been experimentally verified in numerous experiments. It provides a mathematical framework for understanding the probabilistic nature of quantum measurements and the behavior of quantum systems, School Analytics, which can exhibit phenomena such as superposition and entanglement that are not observed in classical physics.