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The damped harmonic oscillator in deformation quantization
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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\"{o}dinger 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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Cited by 2 Pith papers
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First Principles Quantization of a Non-Conservative Scalar Field
A damped scalar field is quantized via doubled variables; the path-integral propagators match in-in results, but the canonical quantization has an internal inconsistency.
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The Feynman-Kac formula in deformation quantization
The ground state energy of a quantum system is extracted from the large imaginary-time limit of the phase space integral of the star exponential of the Hamiltonian, a reformulation of the trace formula.
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