Journal of Physical Mathematics

Models of damped oscillators in quantum mechanics

Ricardo Cordero-Soto, Erwin Suazo, and Sergei K. Suslov

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We consider several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schrödinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time evolution of the expectation values of the energy-related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator.

Article information

J. Phys. Math., Volume 1 (2009), Article ID S090603, 16 pages.

First available in Project Euclid: 25 October 2010

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Zentralblatt MATH identifier

Primary: 81Q05: Closed and approximate solutions to the Schrödinger, Dirac, Klein- Gordon and other equations of quantum mechanics 35C05: Solutions in closed form 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

damped oscillators quantum mechanics Schrödinger equation


Cordero-Soto, Ricardo; Suazo, Erwin; Suslov, Sergei K. Models of damped oscillators in quantum mechanics. J. Phys. Math. 1 (2009), Article ID S090603, 16 pages. doi:10.4303/jpm/S090603.

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