Feynman Path Integral and Schwinger Method for Time-Dependent Mass Harmonic Oscillators

M Sabir, Sundararaman Rajagopalan

Sergio A Albeverio, Sonia Mazzucchi

Surarit Pepore, Bodinchat Sukbot

Surarit Pepore, Bodinchat Sukbot

The exact propagator for a harmonic oscillator with mass growing like m(1+ατ )2 where m and α are constants and τ is time, is derived by the Schwinger method and the Feynman path integral. In the Schwinger formalism, the propagator can be calculated by basic operator algebra and elementary integrations. In the Feynman path integral method, it can be shown that such a propagator can be evaluated from that for a classical action with the application of a Pauli-Van Vleck formula.

Sergio A Albeverio, Raphael J. Høegh-Krohn

Surarit Pepore

In this paper, the propagator for a harmonic oscillator with mass obeying the function of m(t)=mtan2νt is derived by the Feynman path integral method. The wave function of this oscillator is calculated by expanding the obtained propagator. The propagator for a harmonic oscillator with strongly pulsating mass is evaluated by the Schwinger method. The propagator for a harmonic oscillator with mass rapidly growing with time is calculated by applying the integrals of the motion of quantum systems. The comparison between these methods are also discussed.