Exact propagator for a time−dependent harmonic oscillator with and without a singular perturbation

Abstract

By using Feynman’s definition of a path integral, exact propagators for a time−dependent harmonic oscillator with and without an inverse quadratic potential have been evaluated. It is shown that these propagators depend only on the solutions of the classical unperturbed oscillator. The relations between these propagators, the invariants, and the Schrödinger equation are also discussed.