Quantum gaps and classical orbits in a rotating two-dimensional harmonic oscillator

1994 ◽  
Vol 27 (15) ◽  
pp. L553-L558 ◽  
Author(s):  
R K Bhaduri ◽  
Shuxi Li ◽  
K Tanaka ◽  
J C Waddington
Keyword(s):  
Harmonic Oscillator ◽  
Two Dimensional ◽  
Classical Orbits

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.

Probabilistic aspects of the SU(2)-harmonic oscillator

2000 ◽  
Vol 37 (1) ◽  
pp. 306-314
Author(s):  
Shunlong Luo
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Probability Distributions ◽  
Quantum Probability ◽  
Dimensional Sphere ◽  
Large Radius ◽  
Two Dimensional ◽  
Bargmann Transform ◽  
Gaussian Distributions ◽  
Binomial Distributions

In the framework of quantum probability, we present a simple geometrical mechanism which gives rise to binomial distributions, Gaussian distributions, Poisson distributions, and their interrelation. More specifically, by virtue of coherent states and a toy analogue of the Bargmann transform, we calculate the probability distributions of the position observable and the Hamiltonian arising in the representation of the classic group SU(2). This representation may be viewed as a constrained harmonic oscillator with a two-dimensional sphere as the phase space. It turns out that both the position observable and the Hamiltonian have binomial distributions, but with different asymptotic behaviours: with large radius and high spin limit, the former tends to the Gaussian while the latter tends to the Poisson.

Coherent states for Smorodinsky-Winternitz potentials

Open Physics ◽  
2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Nuri Ünal
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Wave Packets ◽  
Harmonic Oscillators ◽  
Polar Coordinates ◽  
Two Dimensional ◽  
Cartesian Coordinates ◽  
Physical Time ◽  
First Case

AbstractIn this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem. In the first case, we find the non-spreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three non-isotropic harmonic oscillators. All of these states evolve in physical-time. We also show that in parametric-time, the second case can be transformed to the first one with vanishing eigenvalues.

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