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The damped harmonic oscillator in deformation quantization

Giuseppe Dito·Francisco Turrubiates
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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.

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Giuseppe Dito, Francisco Turrubiates. 2005-10-19. The damped harmonic oscillator in deformation quantization. https://doi.org/10.1016/j.physleta.2005.12.013

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