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Journal of Mathematical Physics

On the path integral quantization of the damped harmonic oscillator

Christopher C. Gerry

Published Jun 1, 1984• 17 citations
Publisher

Abstract

A time-dependent canonical transformation is performed in the path integral expression of the propagator for a damped harmonic oscillator to reduce it to a harmonic oscillator with modified frequency. The transformation is carried out in a properly time-symmetrized expression of the lattice space path integral by making expansions about the midpoint of each time interval.

DOI
10.1063/1.526361

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Journal of Humanities and Social Sciences Thonburi University•Jan 1, 2014•0 citations
A time-dependent canonical transformation is performed in the path integral expression of the propagator for a damped harmonic oscillator to reduce it to a harmonic oscillator with modified frequency. The transformation is carried out in a properly time-symmetrized expression of the lattice space path integral by making expansions about the midpoint of each time interval.
Using the Caldirola-Kanai Hamiltonian for the quantum dissipative system, the author expresses the propagator as the modified Feynman path integral in the configuration space, which can then be evaluated for the damped harmonic oscillator by Montroll's method. The propagator of the damped harmonic oscillator can also be calculated beyond and at caustics with the help of Horvathy-Feynman formula. The new results are confirmed by investigating the classical paths joining two fixed end-point positions, Finally the author obtains the time-dependent wavefunctions from the propagator of the dynamical system.