ScienceAsia 32 (2006): 173-179 |doi: 10.2306/scienceasia1513-1874.2006.32.173

Path Integral for a Harmonic Oscillator with
Time-Dependent Mass and Frequency

Surarit Pepore,^a* Pongtip Winotai,^a Tanakorn Osotchan^b and Udom Robkob^b

 
ABSTRACT: 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.

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a Department of Chemistry, Faculty of Science, Mahidol University, Rama VI Road, Bangkok 10400, Thailand.
b Department of Physics, Faculty of Science, Mahidol University, Rama VI Road, Bangkok 10400, Thailand.

*,** Corresponding author, E-mail: g4437430@student.mahidol.ac.th

Received 18 Oct 2004, Accepted 6 Feb 2006