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College Physics

Quantum invariant treatment of a time-dependent damped harmonic oscillator

Ling Rui-liang

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Using the canonical transformation and Lewis and Riesenfeld quantum invariant theory,the excat wave function of a harmonic oscillator with time-dependent coefficient of damping is obtained.The exactitude and universallity of wave function are discussed also.

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A systematic way of treating a general time-dependent harmonic oscillator in classical and quantum mechanics is given. By a general canonical transformation in classical mechanics, the time-dependent Hamiltonian can be transformed to a time-independent one (the Lewis-Riesenfeld invariant), explicitly separating a total time-derivative term. In quantum mechanics, one can obtain the phase of the wave function straightforwardly from this total-derivative term, together with the corresponding time-independent Hamiltonian. We solve analytically and algebraically the general time-dependent harmonic oscillator driven by a time-dependent inverse cubic force as an example.