The Born rule assigns probability to outcome when a normalized state is measured in an orthonormal eigenbasis.
Every bijection of pure-state rays that preserves transition probabilities is induced by either a unitary or an antiunitary operator on the Hilbert space.
Because state vectors differing by a quantum phase represent the same ray, a unitary realization of a group action need only satisfy
An ideal energy measurement returns an eigenvalue of the Hamiltonian with probability equal to the squared norm of the state's projection onto its eigenspace. After obtaining a nondegenerate energy, the state is the corresponding energy eigenstate.
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The Born rule is a fundamental principle in quantum mechanics that provides a way to calculate the probability of finding a quantum system in a particular state after a measurement is made. It was formulated by the physicist Max Born in 1926 and is a key element in the interpretation of quantum mechanics.
