Derivation of quantum propagator for coupled harmonic oscillator with uniform electric field in a single harmonic oscillator environment using white noise functional approach

Abstract

The use of white noise analysis is utilized in this study. We consider an open quantum system of coupled harmonic oscillator with uniform two dimensional electric field in a single harmonic oscillator environment. We obtain the quantum propagator for the said system by considering the Feynman path integral as a white noise functional. In addition, the resulting quantum propagator was consistent with the previous literature and also, this study gives more general form due to the inclusion of the electric field. Keywords: Harmonic oscillator, Quantum propagator, Feynman path integral, White noise functional, Lagrangian