scholarly journals Length in a Noncommutative Phase Space

2018 ◽  
Vol 63 (2) ◽  
pp. 102 ◽  
Author(s):  
Kh. P. Gnatenko ◽  
V. M. Tkachuk
Keyword(s):  
Phase Space ◽  
Lower Bound ◽  
Eigenvalue Problem ◽  
Minimal Length ◽  
Uncertainty Relations ◽  
Noncommutative Phase Space

We study restrictions on the length in a noncommutative phase space caused by noncommutativity. The uncertainty relations for coordinates and momenta are considered, and the lower bound of the length is found. We also consider the eigenvalue problem for the squared length operator and find the expression for the minimal length in the noncommutative phase space.

scholarly journals Noncommutative Phase Space Schrödinger Equation with Minimal Length

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Hassanabadi ◽  
Z. Molaee ◽  
S. Zarrinkamar
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
External Magnetic Field ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
Minimal Length ◽  
Two Dimensional ◽  
Noncommutative Phase Space ◽  
Energy Eigenvalues

We consider the Schrödinger equation under an external magnetic field in two-dimensional noncommutative phase space with an explicit minimal length relation. The eigenfunctions are reported in terms of the Jacobi polynomials, and the explicit form of energy eigenvalues is reported.

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.

scholarly journals Algebraic Approach to Exact Solution of the (2 + 1)-Dimensional Dirac Oscillator in the Noncommutative Phase Space

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
H. Panahi ◽  
A. Savadi
Keyword(s):  
Exact Solution ◽  
Phase Space ◽  
Algebraic Approach ◽  
Wave Functions ◽  
Dirac Oscillator ◽  
Noncommutative Phase Space ◽  
Energy Eigenvalues ◽  
Good Agreement

We study the (2 + 1)-dimensional Dirac oscillator in the noncommutative phase space and the energy eigenvalues and the corresponding wave functions of the system are obtained through the sl(2) algebraization. It is shown that the results are in good agreement with those obtained previously via a different method.

scholarly journals Remarks on the uncertainty relations

2020 ◽  
Vol 35 (26) ◽  
pp. 2050219 ◽  
Author(s):  
Krzysztof Urbanowski
Keyword(s):  
Lower Bound ◽  
Characteristic Time ◽  
Uncertainty Relation ◽  
Uncertainty Relations ◽  
Rigorous Analysis ◽  
Standard Deviations ◽  
Complete Sets

We analyze general uncertainty relations and we show that there can exist such pairs of non-commuting observables [Formula: see text] and [Formula: see text] and such vectors that the lower bound for the product of standard deviations [Formula: see text] and [Formula: see text] calculated for these vectors is zero: [Formula: see text]. We also show that for some pairs of non-commuting observables the sets of vectors for which [Formula: see text] can be complete (total). The Heisenberg, [Formula: see text], and Mandelstam–Tamm (MT), [Formula: see text], time–energy uncertainty relations ([Formula: see text] is the characteristic time for the observable [Formula: see text]) are analyzed too. We show that the interpretation [Formula: see text] for eigenvectors of a Hamiltonian [Formula: see text] does not follow from the rigorous analysis of MT relation. We show also that contrary to the position–momentum uncertainty relation, the validity of the MT relation is limited: It does not hold on complete sets of eigenvectors of [Formula: see text] and [Formula: see text].

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 Thermodynamical properties of graphene in noncommutative phase–space

2014 ◽  
Vol 349 ◽  
pp. 402-410 ◽  
Author(s):  
Victor Santos ◽  
R.V. Maluf ◽  
C.A.S. Almeida
Keyword(s):  
Phase Space ◽  
Noncommutative Phase Space ◽  
Thermodynamical Properties

A LOWER BOUND FOR THE BUCKLING LOAD OF A DIVERGENT NON-CONSERVATIVE SYSTEM

1988 ◽  
Vol 12 (3) ◽  
pp. 129-132
Author(s):  
B.L. LY
Keyword(s):  
Lower Bound ◽  
Eigenvalue Problem ◽  
Adjoint System ◽  
Conservative System ◽  
Buckling Load ◽  
Smallest Eigenvalue

The divergent non-conservative problems considered in this paper are pseudo self-adjoint. It is shown that a self-adjoint eigenvalue problem is related to the original non-conservative problem. The smallest eigenvalue of this self-adjoint system provides a lower bound for the buckling load of the non-conservative system.

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