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Journal of Physics A Mathematical and General

Thermodynamics of the standard quantum harmonic oscillator of time-dependent frequency with and without inverse quadratic potential

Jeong-Ryeol Choi, Shou Zhang

Published Mar 15, 2002• 11 citations
Publisher

Abstract

Making use of a dynamical invariant operator, we obtain a quantum mechanical solution of a damped harmonic oscillator having time-dependent frequency with and without inverse quadratic potential. We confirm that the uncertainty relation is always larger than ℏ/2 in both the number and thermal state. We obtain a density operator satisfying the Liouville-von Neumann equation, and use its diagonal elements to calculate various expectation values in the thermal state.

DOI
10.1088/0305-4470/35/12/309

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Making use of a dynamical invariant operator, we obtain a quantum mechanical solution of a damped harmonic oscillator having time-dependent frequency with and without inverse quadratic potential. We confirm that the uncertainty relation is always larger than ℏ/2 in both the number and thermal state. We obtain a density operator satisfying the Liouville-von Neumann equation, and use its diagonal elements to calculate various expectation values in the thermal state.
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