Equivalence of time-dependent variational descriptions of quantum systems and Hamilton's mechanics

Abstract

It is shown that any time-dependent description of quantum systems derived from the variational principle is equivalent to Hamilton's description of a classical system. This is done by establishing the fact that the Euler's equations from the variation of the wave function in any parametrization can be transformed to a system of Hamilton's equations. The problem of obtaining collective dynamical variables in quantum many-body systems is discussed in the light of this equivalence.