Schwinger Method and Path Integral with Generalized Canonical Transformation for a Harmonic Oscillator with Time-Dependent Mass and Frequency

Surarit Pepore；Bodinchat Sukbot

Chinese Journal of Physics

47卷6期（2009 / 12 / 01）

753 - 763

英文

The exact propagator for a harmonic oscillator with time-dependent mass and frequency is found by the Schwinger method and a path integral with a generalized canonical transformation. In the Schwinger formalism, the propagator can be obtained by basic operator algebra and elementary integrations. In the path integral method, it can be shown that such a propagator can be derived from that for a unit mass and frequency oscillator in a new space-time coordinate system with the help of a generalized canonical transformation. The power of propagator methods for solving time-dependent Hamiltonian systems is also discussed.