scholarly journals Extended Wigner function for the harmonic oscillator in the phase space

2020 ◽  
Vol 19 ◽  
pp. 103546
Author(s):  
E.E. Perepelkin ◽  
B.I. Sadovnikov ◽  
N.G. Inozemtseva ◽  
E.V. Burlakov
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Wigner Function

Scale transformations in phase space and stretched states of a harmonic oscillator

2017 ◽  
Vol 192 (1) ◽  
pp. 1080-1096 ◽  
Author(s):  
V. A. Andreev ◽  
D. M. Davidović ◽  
L. D. Davidović ◽  
Milena D. Davidović ◽  
Miloš D. Davidović
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Scale Transformations

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

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 180 ◽  
Author(s):  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Canonical Quantization ◽  
Extended Phase Space ◽  
Two Dimensional ◽  
Class Constraint ◽  
Extended Phase ◽  
Damped Harmonic Oscillator ◽  
Points Of View ◽  
Space Description

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.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

Quantum uncertainties of the confined Harmonic Oscillator in position, momentum and phase-space

2014 ◽  
Vol 526 (11-12) ◽  
pp. 555-566 ◽  
Author(s):  
Humberto G. Laguna ◽  
Robin P. Sagar
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator
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