Exact Quantum Solutions for Time-Dependent Charged Oscillator

Abstract

The quantum states for a time-dependent charged oscillator are investigated by an invariant operator method and a unitary transformation approach. The wave functions are derived precisely in both cases of discrete and continuous quantum spectra. By choosing time functions of the Hamiltonian in different forms, our theory can be applied to diverse types of quantum dynamical systems. In the limit of a simple case, we confirmed that our result associated with a discrete spectrum recovers to that of Storchak.