Lewis-Riesenfeld quantization and SU(1,1) coherent states for 2D damped harmonic oscillator

Abstract

In this paper we study a two-dimensional [2D] 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 mean of the solutions we verify a generalization version of the Heisenberg's uncertainty relation and derive the generators of the $su(1,1)$ Lie algebra. Based on these generators, we construct the coherent states $\grave{\text{a}}$ la Barut-Girardello and $\grave{\text{a}}$ la Perelomov and respectively study their properties.

27 pages

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• Generalized $su(1,1)$ coherent states for pseudo harmonic oscillator and their nonclassical properties
• Fast and stable manipulation of a charged particle in a Penning trap
• Applications of the group SU(1,1) for quantum computation and tomography
• Landau problem with a general time-dependent electric field
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• Squeezed coherent states for gravitational well in noncommutative space
• Lewis and Berry phases for a gravitational wave interacting with a quantum harmonic oscillator
• Dirac's Method for the Two-Dimensional Damped Harmonic Oscillator in the Extended Phase Space
• Quantization of nonlinear non-Hamiltonian systems
• Tuning the separability in noncommutative space
• Time-dependent conserved operators for autonomous systems and quantization of resistance