Ehrenfest’s theorem and nonclassical states of light: 1. Ehrenfest’s theorem in quantum mechanic

Abstract

When it was first enunciated, Ehrenfest’s Theorem provided a necessary and important link between classical mechanics and quantum mechanics. Today, the content of the theorem is understood to be a natural and immediate consequence of the equation of motion for operators when quantum mechanics is formulated in the Heisenberg picture. Nevertheless, the theorem leads to useful approximations when systems with Hamiltonians of higher than quadratic order in the dynamical variables are considered. In this two-part article, we use it to provide a convenient illustration of the differences between so-called classical and nonclassical states of radiation.