Metaplectic operator approach to a time-dependent generalized harmonic oscillator

Abstract

The metaplectic operator is a unitary operator corresponding to a time-dependent classical linear canonical transformation. We present the explicit expression for the metaplectic operator. The parameter in the metaplectic operator is expressed in terms of the solution of a classical time-dependent generalized harmonic oscillator. The time evolution operator, Lewis and Riesenfeld invariant, and the wave function of the time-dependent generalized harmonic oscillator are studied using the metaplectic operator, and the results are compared with those from other studies. The metaplectic operator method is a simpler method for studying the time-dependent generalized harmonic oscillator.