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 Schr\"odinger 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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