scholarly journals Uncertainty relations for a non-canonical phase-space noncommutative algebra

2019 ◽  
Vol 52 (22) ◽  
pp. 225203 ◽  
Author(s):  
Nuno C Dias ◽  
João N Prata
Keyword(s):  
Phase Space ◽  
Uncertainty Relations ◽  
Noncommutative Algebra

scholarly journals Composite system in rotationally invariant noncommutative phase space

2018 ◽  
Vol 33 (07) ◽  
pp. 1850037 ◽  
Author(s):  
Kh. P. Gnatenko ◽  
V. M. Tkachuk
Keyword(s):  
Phase Space ◽  
Composite System ◽  
Particle System ◽  
Rotational Symmetry ◽  
Center Of Mass ◽  
Noncommutative Space ◽  
Effective Parameters ◽  
Noncommutative Phase Space ◽  
Noncommutative Algebra ◽  
Rotationally Invariant

Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of composite system reproduce noncommutative algebra for coordinates and momenta of individual particles. Also, on these conditions, the coordinates and the momenta of the center-of-mass satisfy noncommutative algebra with effective parameters of noncommutativity which depend on the total mass of the system and do not depend on its composition. Besides, it is shown that on these conditions the coordinates in noncommutative space do not depend on mass and can be considered as kinematic variables, the momenta are proportional to mass as it has to be. A two-particle system with Coulomb interaction is studied and the corrections to the energy levels of the system are found in rotationally invariant noncommutative phase space. On the basis of this result the effect of noncommutativity on the spectrum of exotic atoms is analyzed.

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.

scholarly journals Noncommutative phase space with rotational symmetry and hydrogen atom

2017 ◽  
Vol 32 (26) ◽  
pp. 1750161 ◽  
Author(s):  
Kh. P. Gnatenko ◽  
V. M. Tkachuk
Keyword(s):  
Phase Space ◽  
Hydrogen Atom ◽  
Rotational Symmetry ◽  
Energy Levels ◽  
Upper Bounds ◽  
Second Order ◽  
Noncommutative Phase Space ◽  
Noncommutative Algebra ◽  
Canonical Type ◽  
Rotationally Invariant

We construct algebra with noncommutativity of coordinates and noncommutativity of momenta which is rotationally invariant and equivalent to noncommutative algebra of canonical type. Influence of noncommutativity on the energy levels of hydrogen atom is studied in rotationally invariant noncommutative phase space. We find corrections to the levels up to the second order in the parameters of noncommutativity and estimate the upper bounds of these parameters.

scholarly journals NEGATIVE PROBABILITY AND UNCERTAINTY RELATIONS

2001 ◽  
Vol 16 (37) ◽  
pp. 2381-2385 ◽  
Author(s):  
THOMAS CURTRIGHT ◽  
COSMAS ZACHOS
Keyword(s):  
Phase Space ◽  
Uncertainty Relations ◽  
Marginal Distributions ◽  
Negative Probability ◽  
Direct Use

A concise derivation of all uncertainty relations is given entirely within the context of phase-space quantization, without recourse to operator methods, to the direct use of Weyl's correspondence, or to marginal distributions of x and p.

scholarly journals Harmonic Oscillator Chain in Noncommutative Phase Space with Rotational Symmetry

2019 ◽  
Vol 64 (2) ◽  
pp. 131
Author(s):  
Kh. P. Gnatenko
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Rotational Symmetry ◽  
Center Of Mass ◽  
Quantum Space ◽  
Noncommutative Phase Space ◽  
Noncommutative Algebra ◽  
A Chain ◽  
Rotationally Invariant

We consider a quantum space with a rotationally invariant noncommutative algebra of coordinates and momenta. The algebra contains the constructed tensors of noncommutativity involving additional coordinates and momenta. In the rotationally invariant noncommutative phase space, the harmonic oscillator chain is studied. We obtain that the noncommutativity affects the frequencies of the system. In the case of a chain of particles with harmonic oscillator interaction, we conclude that, due to the noncommutativity of momenta, the spectrum of the center-of-mass of the system is discrete and corresponds to the spectrum of a harmonic oscillator.

scholarly journals COMMUTATOR ANOMALY IN NONCOMMUTATIVE QUANTUM MECHANICS

2006 ◽  
Vol 21 (39) ◽  
pp. 2971-2976 ◽  
Author(s):  
SAYIPJAMAL DULAT ◽  
KANG LI
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Uncertainty Relation ◽  
Uncertainty Relations ◽  
Noncommutative Phase Space ◽  
Noncommutative Quantum Mechanics ◽  
Physical Observable ◽  
Noncommutative Quantum

In this paper, the Schrödinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space–space and space–momentum as well as momentum–momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.

On uncertainty relations in noncommutative phase space

Open Physics ◽  
2010 ◽  
Vol 8 (1) ◽  
Author(s):  
Guangjie Guo ◽  
Chaoyun Long ◽  
Shuijie Qin
Keyword(s):  
Phase Space ◽  
Natural Condition ◽  
Uncertainty Relations ◽  
Noncommutative Phase Space ◽  
Noncommutative Plane

AbstractThe uncertainty relations are discussed on a noncommutative plane when noncommutativity of momentum spaces is considered. It is possible to construct normalizable states by simultaneously saturating two coordinate-momentum uncertainty relations. However, under the natural condition θη ≪ 4ħ2 one can not construct a normalizable state by simultaneously saturating any other pairs out of four basic nontrivial uncertainty relations.

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