Dirac’s Method for the Two-Dimensional Damped Harmonic Oscillator in the Extended Phase Space

Laure Gouba
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Laure Gouba: The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34151 Trieste, Italy

Mathematics, 2018, vol. 6, issue 10, 1-10

Abstract: The system of a two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem that has already been addressed by many authors that we present here with some fresh points of view and carry on a whole discussion. We show that the system is singular. The classical Hamiltonian is proportional to the first-class constraint. We pursue with the Dirac’s canonical quantization procedure by fixing the gauge and provide a reduced phase space description of the system. As a result, the quantum system is simply modeled by the original quantum Hamiltonian.

Keywords: damped harmonic oscillator; extended phase space; constrained system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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