Observables correspond to hermitian operators from "summary" of The Principles of Quantum Mechanics by P. A. M. Dirac
Observables in quantum mechanics are represented by physical quantities that are measurable, such as position, momentum, energy, and angular momentum. In the mathematical formalism of quantum mechanics, observables are associated with operators. These operators act on the wave function of a system and yield the values of the corresponding observable when applied to the wave function. Hermitian operators play a crucial role in quantum mechanics because they are associated with observables. The eigenvalues of a Hermitian operator correspond to the possible outcomes of measurements of the observable it represents. When a measurement is performed on a system in a particular state, the system will collapse into one of the eigenstates of the Hermitian operator, with the corresponding eigenvalue being the result of the measurement. The requirement for observables to correspond to Hermitian operators stems from the postulates of quantum mechanics. According to these postulates, the physical state of a system is described by a wave function, and observables are represented by operators that act on the wave function. The operators corresponding...
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