Integrals of the motion and Green function for dual damped oscillators and coupled harmonic oscillators

Abstract

The application for the integrals of the motion of a quantum system in deriving Green function or propagator is presented. The Green function is shown to be the eigenfunction of the integrals of the motion which described initial points of the system trajectory in the phase space. The exact expressions for the Green functions of the dual damped oscillators and the coupled harmonic oscillators are evaluated in co-ordinate representations. The relation between the integrals of the motion method and other methods such as Feynman path integral and Schwinger method are also presented.

The propagators for time-dependent mass harmonic oscillators

“…14 In 2018, S Pepore applied the integrals of the motion of quantum systems to calculate the Green function for time-dependent mass harmonic oscillators, 15 dual damped oscillators, and coupled harmonic oscillators. 16 The final aims of this paper is employing this method to calculate the propagator for a harmonic oscillator with mass rapidly growing with time…”

Propagators for a particle in a time-dependent linear potential and a free particle

“…In 2018, S. Pepore applied the integrals of the motion to calculate the propagators for time-dependent harmonic oscillators. 8,9 The one aim of this article is applying the integrals of the motion to derive the propagators for a particle moving in a timedependent linear potential and a free particle with linear damping. The organization of this paper are as follows.…”