Feynman Path Integral to Van Vleck Propagator

Eric Heller

Plamen Fiziev

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.

E. Badralexe

For a general time-dependent and the Bateman-Morse-Feshbach-Bopp Lagrangian the Feynman path integral is evaluated by establishing a polynomial representation of the Van Vleck determinant.