The measurement postulate, also known as the projection postulate or the Born rule, is a fundamental concept in quantum mechanics that describes the outcome and probabilities of measuring a quantum system. This postulate addresses the probabilistic nature of quantum mechanics and provides a framework for predicting the results of measurements on quantum systems.
According to the measurement postulate:
When a measurement is made on a quantum system, the result corresponds to one of the eigenvalues of the observable being measured. An observable is a physical quantity, such as position, momentum, or energy, represented by a Hermitian operator in quantum mechanics.
The probability of obtaining a particular eigenvalue is given by the squared magnitude of the corresponding eigenvector's component (also known as the probability amplitude) in the quantum system's state vector. This is referred to as the Born rule.
After the measurement, the quantum system collapses (or projects) onto the eigenvector associated with the measured eigenvalue, resulting in a definite state for the system. This is known as the wave function collapse.
The measurement postulate is essential in understanding the inherently probabilistic nature of quantum mechanics and the seemingly random outcomes of measurements on quantum systems. It also helps to explain the transition from the quantum realm's superposition states to the definite classical states we observe in everyday life.