Ehrenfest’s theorem makes expectation values obey Hamiltonian commutator equations analogous to classical motion.
For , the canonical commutation relation givesThese are the expectation-value analogues of Newton's second law and conservation of energy.
The correspondence principle states that quantum predictions approach classical mechanics in the appropriate large-scale or semiclassical regime.
Articles by others on the same topic
The Ehrenfest theorem is a fundamental result in quantum mechanics that relates the time evolution of the expected values (or expectation values) of quantum observables to classical mechanics. It essentially bridges the gap between classical and quantum dynamics.