Path Integral and Space-Time Transformations for Time-Dependent Hamiltonian Systems

Abstract

The exact solutions for the time-dependent Hamiltonian systems is studied by the Feynman path integral method. The quantum mechanical propagator of a harmonic oscillator with strongly pulsating mass is calculated by the Pauli-Van Vleck formula while the wave functions is derived from the spectral representation of the obtained propagator. We demonstrate that the use of a space-time transformation can simplify the evaluation of the propagator for a time-dependent linear potential. We also show that such a propagator can be obtained from the free-particle propagator in the new space-time coordinate system.