Publication: Path integral for a harmonic oscillator with time-dependent mass and frequency
Issued Date
2006-06-01
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ISSN
15131874
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2-s2.0-33746039658
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Mahidol University
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SCOPUS
Bibliographic Citation
ScienceAsia. Vol.32, No.2 (2006), 173-179
Suggested Citation
Surarit Pepore, Pongtip Winotai, Tanakom Osotchan, Udom Robkob Path integral for a harmonic oscillator with time-dependent mass and frequency. ScienceAsia. Vol.32, No.2 (2006), 173-179. doi:10.2306/scienceasia1513-1874.2006.32.173 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/23946
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Title
Path integral for a harmonic oscillator with time-dependent mass and frequency
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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.