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The damped harmonic oscillator in deformation quantization

Giuseppe DitoFrancisco J. Turrubiates

subject

High Energy Physics - TheoryDeformation quantization[ PHYS.QPHY ] Physics [physics]/Quantum Physics [quant-ph]Canonical quantizationGeneral Physics and AstronomyFOS: Physical sciences01 natural sciences[ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th]Poisson bracket[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]Quantum mechanics0103 physical sciencesdissipative systems010306 general physicsNonlinear Sciences::Pattern Formation and Solitonsquantum mechanics.Harmonic oscillatorEigenvalues and eigenvectorsPhysicsQuantum Physics010308 nuclear & particles physics[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]Quantization (signal processing)quantum mechanicsPACS numbers: 03.50.-z 03.50.De 11.10.-z 03.65.DbLandau quantization16. Peace & justiceSecond quantizationClassical mechanicsHigh Energy Physics - Theory (hep-th)Schrödinger pictureQuantum Physics (quant-ph)

description

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.

yearjournalcountryeditionlanguage
2005-10-19
https://hal.archives-ouvertes.fr/hal-00012298/file/dito-turrubiates.pdf