Exact propagator of the harmonic oscillator with a time-dependent mass

Voranuch Thongpool, Surarit Pepore

Swapan Kumar Mandal

CELIA M. A. DANTAS, I. A. Pedrosa, B. Baseia

Bancha Kirdmanee, Surarit Pepore, Bodinchat Sukbot

We demonstrate that the use of a space-time transformation in path integral can simplify the calculation of the propagator for a harmonic oscillator with time-dependent mass and frequency. We show that such a propagator can be easily obtained from the unit mass and frequency propagator in the new space-time coordinate systems. Two cases of harmonic oscillator with time-dependent mass, which exact propagator can be evaluated, are investigated.

Surarit Pepore, P. Winotai, Tanakorn Osotchan +1 more

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.

Carlos Farina de Souza, ALVARO DE SOUZA DUTRA