QUANTUM REPRESENTATION OF A TIME-DEPENDENT QUADRATIC HAMILTONIAN IN ATIME-DEPENDENT PHASE-SPACE FRAME

A comoving reference frame in phase space is introduced in order to an alyze the behaviour of time-dependent multi-dimensional quadratic Hami ltonians. 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 Wi gner functions of such systems can be cast into factorized time-indepe ndent form by the introduction of appropriate time-dependent coordinat es related to its integrals of motion is explained.