scholarly journals CONSISTENT DEFORMED BOSONIC ALGEBRA IN NONCOMMUTATIVE QUANTUM MECHANICS

2008 ◽  
Vol 23 (09) ◽  
pp. 1393-1403 ◽  
Author(s):  
JIAN-ZU ZHANG
Keyword(s):  
Quantum Mechanics ◽  
Weyl Algebra ◽  
Fock Space ◽  
General Relation ◽  
Noncommutative Space ◽  
Two Dimensional ◽  
Noncommutative Quantum Mechanics ◽  
Commutative Space ◽  
Creation Operators ◽  
Noncommutative Quantum

In two-dimensional noncommutative space for the case of both position–position and momentum–momentum noncommuting, the consistent deformed bosonic algebra at the nonperturbation level described by the deformed annihilation and creation operators is investigated. A general relation between noncommutative parameters is fixed from the consistency of the deformed Heisenberg–Weyl algebra with the deformed bosonic algebra. A Fock space is found, in which all calculations can be similarly developed as if in commutative space and all effects of spatial noncommutativity are simply represented by parameters.

scholarly journals NONCOMMUTATIVE QUANTUM MECHANICS: THE TWO-DIMENSIONAL CENTRAL FIELD

2002 ◽  
Vol 17 (19) ◽  
pp. 2555-2565 ◽  
Author(s):  
J. GAMBOA ◽  
F. MÉNDEZ ◽  
M. LOEWE ◽  
J. C. ROJAS
Keyword(s):  
Quantum Mechanics ◽  
Central Field ◽  
Two Dimensional ◽  
Limit Case ◽  
Polynomial Type ◽  
Noncommutative Quantum Mechanics ◽  
The Green Function ◽  
Noncommutative Plane ◽  
Noncommutative Quantum ◽  
Noncommutative Parameter

Quantum mechanics in a noncommutative plane is considered. For a general two-dimensional central field, we find that the theory can be perturbatively solved for large values of the noncommutative parameter (θ) and explicit expressions for the eigenstates and eigenvalues are given. The Green function is explicitly obtained and we show that it can be expressed as an infinite series. For polynomial type potentials, we found a smooth limit for small values of θ and for nonpolynomial ones this limit is necessarily abrupt. The Landau problem, as a limit case of a noncommutative system, is also considered.

scholarly journals LAPLACE-RUNGE-LENZ VECTOR IN QUANTUM MECHANICS IN NONCOMMUTATIVE SPACE

2014 ◽  
Vol 54 (2) ◽  
pp. 149-155
Author(s):  
Peter Prešnajder ◽  
Veronika Gáliková ◽  
Samuel Kováčik
Keyword(s):  
Quantum Mechanics ◽  
Hydrogen Atom ◽  
Configuration Space ◽  
Dynamical Symmetry ◽  
Rotational Invariance ◽  
Noncommutative Space ◽  
Noncommutative Quantum Mechanics ◽  
Noncommutative Quantum

The object under scrutiny is the dynamical symmetry connected with conservation of the Laplace-Runge-Lenz vector (LRL) in the hydrogen atom problem solved by means of noncommutative quantum mechanics (NCQM). The considered noncommutative configuration space has such a “fuzzy”<br />structure that the rotational invariance is not spoilt. An analogy with the LRL vector in the NCQM is brought to provide our results and also a comparison with the standard QM predictions.

Energy-dependent harmonic oscillator in noncommutative space

2017 ◽  
Vol 32 (20) ◽  
pp. 1750106 ◽  
Author(s):  
A. Benchikha ◽  
M. Merad ◽  
T. Birkandan
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Polar Coordinates ◽  
Noncommutative Space ◽  
Normalization Condition ◽  
Potential Yield ◽  
Noncommutative Quantum Mechanics ◽  
Dependent Mass ◽  
Energy Dependent ◽  
Noncommutative Quantum

In noncommutative quantum mechanics, the energy-dependent harmonic oscillator problem is studied by solving the Schrödinger equation in polar coordinates. The presence of the noncommutativity in space coordinates and the dependence on energy for the potential yield energy-dependent mass and potential. The correction of normalization condition is calculated and the parameter-dependences of the results are studied graphically.

Two-dimensional noncommutative quantum mechanics with the central potential

2016 ◽  
Vol 31 (08) ◽  
pp. 1650046
Author(s):  
Won Sang Chung
Keyword(s):  
Quantum Mechanics ◽  
Central Field ◽  
Two Dimensional ◽  
Noncommutative Algebra ◽  
Central Potential ◽  
Noncommutative Quantum Mechanics ◽  
Space Noncommutativity ◽  
Noncommutative Plane ◽  
Noncommutative Quantum ◽  
Noncommutative Parameter

Quantum mechanics in a noncommutative plane with both space noncommutativity and momentum noncommutativity is considered. For a general two-dimensional central field, we show that the theory can be perturbatively solved for large values of the space noncommutative parameter [Formula: see text] when the momentum noncommutative parameter [Formula: see text] is proportional to [Formula: see text]. We obtain the expressions for the eigenstates and eigenvalues. We also discuss the more general noncommutative algebra which have the nonvanishing commutator for [Formula: see text] for different [Formula: see text], [Formula: see text].

scholarly journals From Feynman proof of Maxwell equations to noncommutative quantum mechanics

2007 ◽  
Vol 70 ◽  
pp. 012004 ◽  
Author(s):  
A Bérard ◽  
H Mohrbach ◽  
J Lages ◽  
P Gosselin ◽  
Y Grandati ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Maxwell Equations ◽  
Noncommutative Quantum Mechanics ◽  
Noncommutative Quantum

scholarly journals Non-Hermitian noncommutative quantum mechanics

2019 ◽  
Vol 134 (7) ◽  
Author(s):  
J. F. G. dos Santos ◽  
F. S. Luiz ◽  
O. S. Duarte ◽  
M. H. Y. Moussa
Keyword(s):  
Quantum Mechanics ◽  
Noncommutative Quantum Mechanics ◽  
Noncommutative Quantum

scholarly journals A Noncommutative Model of Cosmology with Two Metrics

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 435
Author(s):  
Horacio Falomir ◽  
Jorge Gamboa ◽  
Fernando Mendez
Keyword(s):  
Quantum Mechanics ◽  
Dark Energy ◽  
Equation Of State ◽  
Point Of View ◽  
Classical Analog ◽  
Noncommutative Quantum Mechanics ◽  
Friedmann Robertson Walker ◽  
Noncommutative Quantum

We propose a bicosmology model which reduces to the classical analog of noncommutative quantum mechanics. From this point of view, one of the sources in the so modified Friedmann-Robertson- Walker equations is a kind of dark energy governed by a Chapligyn-like equation of state. The parameters of noncommutativity θ and B are interpreted in terms of the Planck area and a magnetic-like field, which presumably acts as a seed for magnetogenesis.

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