Phase-space tomography of the truncated harmonic oscillator states

1999 ◽  
Author(s):  
Marta C. Gonzalez ◽  
Celso L. Ladera
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator

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.

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

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

scholarly journals Harmonic oscillator under Lévy noise: Unexpected properties in the phase space

2011 ◽  
Vol 83 (4) ◽  
Author(s):  
Igor M. Sokolov ◽  
Werner Ebeling ◽  
Bartłomiej Dybiec
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Lévy Noise ◽  
Levy Noise

scholarly journals $$\theta(\hat{x},\hat{p})$$ -deformation of the Harmonic Oscillator in a 2D-phase Space

2013 ◽  
pp. 29-37
Author(s):  
M. N. Hounkonnou ◽  
D. Ousmane Samary ◽  
E. Baloïtcha ◽  
S. Arjika
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator

scholarly journals Effect of noncommutativity on the spectrum of free particle and harmonic oscillator in rotationally invariant noncommutative phase space

2018 ◽  
Vol 33 (16) ◽  
pp. 1850091 ◽  
Author(s):  
Kh. P. Gnatenko ◽  
O. V. Shyiko
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Rotational Symmetry ◽  
Free Particle ◽  
Second Order ◽  
Noncommutative Phase Space ◽  
Noncommutative Algebra ◽  
Ordinary Space ◽  
Canonical Type ◽  
Rotationally Invariant

We consider rotationally invariant noncommutative algebra with tensors of noncommutativity constructed with the help of additional coordinates and momenta. The algebra is equivalent to the well-known noncommutative algebra of canonical type. In the noncommutative phase space, rotational symmetry influence of noncommutativity on the spectrum of free particle and the spectrum of harmonic oscillator is studied up to the second-order in the parameters of noncommutativity. We find that because of momentum noncommutativity, the spectrum of free particle is discrete and corresponds to the spectrum of harmonic oscillator in the ordinary space (space with commutative coordinates and commutative momenta). We obtain the spectrum of the harmonic oscillator in the rotationally invariant noncommutative phase space and conclude that noncommutativity of coordinates affects its mass. The frequency of the oscillator is affected by the coordinate noncommutativity and the momentum noncommutativity. On the basis of the results, the eigenvalues of squared length operator are found and restrictions on the value of length in noncommutative phase space with rotational symmetry are analyzed.

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