Quantum representation of a time-dependent quadratic Hamiltonian in a time-dependent phase space frame

Abstract

A comoving reference frame in phase space is introduced in order to analyze the behaviour of time-dependent multi-dimensional quadratic. Hamiltonians. It is found that an explicit (time-dependent) representation exists in which the wave function always remains in a factorized form and independent of time. In this way the previous finding that the Wigner functions of such systems can be cast into factorized time-independent form by the introduction of appropriate time-dependent coordinates related to its integrals of motion is explained.