ehrenfest theorem in quantum mechanics

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ehrenfest theorem in quantum mechanics
The Ehrenfest theorem connects quantum and classical mechanics by showing that the expectation values of quantum mechanical observables, like position and momentum, follow classical equations of motion over time, such as Newton's laws. Mathematically, it states that the time derivative of the expectation value of a general quantum operator is related to the expectation value of the commutator of that operator with the Hamiltonian (total energy) of the system. For position and momentum, this yields equations for the time evolution of their expectation values that are analogous to classical equations, particularly for polynomial potentials.