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Physics Letters A

SU(1, 1) spectrum generating algebra for the quantum damped harmonic oscillator

Vincenzo Barone, Vittorio Penna, Pasquale Sodano

Published Dec 1, 1991• 3 citations
Publisher
DOI
10.1016/0375-9601(91)90541-f

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In this paper, we study a two-dimensional rotationally symmetric harmonic oscillator with time-dependent frictional force. At the classical level, we solve the equations of motion for a particular case of the time-dependent coefficient of friction. At the quantum level, we use the Lewis-Riesenfeld procedure of invariants to construct exact solutions for the corresponding time-dependent Schrödinger equations. The eigenfunctions obtained are in terms of the generalized Laguerre polynomials. By means of the solutions, we verify a generalization version of Heisenberg’s uncertainty relation and derive the generators of the su(1, 1) Lie algebra. Based on these generators, we construct the coherent states à la Barut-Girardello and à la Perelomov and respectively study their properties.