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PREPARATION OF PAPERS FOR JOURNAL SCIENCES & TECHNOLOGIES A.

Badri Berrabah, Baya Bentag

Published Dec 1, 2017• 0 citations
OpenAlex

Abstract

We present a space-time transformation to the harmonic oscillator with a time-dependent mass and frequency and we transform the problem to that of constant mass and time-dependent potential of the form . The propagator and the corresponding wave functions are given. A new general model of time-dependent mass is proposed.

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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.