Untitled

Abstract

The exact solutions to the time-dependent Schrodinger equation for a harmonic oscillator with time-dependent mass and frequency were derived in a general form. The quantum mechanical propagator was calculated by the Feynman path integral method, while the wave function was derived from the spectral representation of the obtained propagator. It was shown that the propagator and the wave function depended on the s solution of a classical oscillator, in which the amplitude and phase satisfied the auxiliary equations. To demonstrate the derivation of the solution from our auxiliary equations, exponential and periodic functions of mass with constant frequency were imposed to evaluate the propagator and wave function for the Caldirola-Kanai and pulsating mass oscillators, respectively.

Integrals of the motion and green functions for time-dependent mass harmonic oscillators

“…Man'ko [4] constructed the Green functions for the driven harmonic oscillator with the aid of integrals of the motion. In the present paper we want to calculate the Green functions or propagators for the damped harmonic oscillator [5][6][7], the harmonic oscillator with strongly pulsating mass, [8] and the harmonic oscillator with mass growing with time [9] by the method developed by V.V. Dodonov et al [3] This paper is organized as follows.…”

The propagators for time-dependent mass harmonic oscillators

“…10 The another method to solve the timedependent harmonic oscillator problems is Feynman path integral. 11,12 The Feynman path integral is the formulation which is invented for calculating the propagator. The propagator represents the transition probability amplitude of the system or Green's function of the Schrodinger's equation.…”

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

“…The standard method in calculating the propagator is Feynman path integral. 1 In 2006, S.Pepore and et al 2 applied the Feynman path integral method to Calculate the propagator for a harmonic oscillator with time-dependent mass and frequency. The one aim of this paper is using the path integral method to derive the propagator for a charged harmonic oscillator in time-dependent electric field.…”