Quantum and Classical Exact Solutions of the Time-Dependent Driven Generalized Harmonic Oscillator

Abstract

Using the trial function method, exact wave functions of the time-dependent driven generalized harmonic oscillator (TDGHO) were derived. The wave functions are wave packets with the center moving according to the classical equation of motion. Correspondingly, the geometrical phase is divided into two parts with one part generated by the shape change of the wave packet and the other part by the motion of the wave packet center. The exact classical solution as well as the classical phase was obtained from a quantum description by the Heisenberg correspondence principle. Finally, the relationship between the quantum and classical phases was achieved.