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

Abstract

The system of two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem already addressed by many authors that we present here in some fresh points of view and carry on smoothly 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 result the quantum system is simply modeled by the original quantum Hamiltonian.

12 pages, Open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0)

References in corpus (3)

• Hamiltonian dynamics on the symplectic extended phase space for autonomous and non-autonomous systems
• Invariants for time-dependent Hamiltonian systems
• Lewis-Riesenfeld quantization and SU(1,1) coherent states for 2D damped harmonic oscillator

Cited by in corpus (2)

• Affine Quantization on the Half Line
• Beyond Coherent State Quantization