The damped harmonic oscillator in deformation quantization

Abstract

We propose a new approach to the quantization of the damped harmonic oscillator in the framework of deformation quantization. The quantization is performed in the Schrödinger picture by a star-product induced by a modified "Poisson bracket". We determine the eigenstates in the damped regime and compute the transition probability between states of the undamped harmonic oscillator after the system was submitted to dissipation.

Plain LaTex file, 11 pages

References in corpus (5)

• Deformation quantization of Poisson manifolds, I
• Quantization of non-Hamiltonian and Dissipative Systems
• Quantum mechanics of damped systems
• States and representations in deformation quantization
• Stationary States of Dissipative Quantum Systems

Cited by in corpus (9)

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• On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator
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• The Weyl-Wigner-Moyal formalism on a discrete phase space. I. A Wigner function for a nonrelativistic particle with spin
• On Wigner functions and a damped star product in dissipative phase-space quantum mechanics
• (1+1) Newton-Hooke Group for the Simple and Damped Harmonic Oscillator
• Deformation Quantization of a Certain Type of Open Systems
• Deformation Quantization of Relativistic Particles in Electromagnetic Fields
• Looking for a time independent Hamiltonian of a dynamical system