Statistical properties of the q-deformed relativistic Dirac oscillator in minimal length quantum mechanics

2018 ◽  
Vol 96 (1) ◽  
pp. 25-29 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W.S. Chung
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
External Magnetic Field ◽  
Relativistic Quantum ◽  
Two Dimensions ◽  
Minimal Length ◽  
Statistical Properties ◽  
Relativistic Quantum Mechanics ◽  
Two Dimensional ◽  
Dirac Oscillator

In this article, we introduce a two-dimensional Dirac oscillator in the presence of an external magnetic field in terms of q-deformed creation and annihilation operators in the framework of relativistic quantum mechanics with minimal length. We discuss the eigenvalues of q-deformed Dirac oscillator in two dimensions and report the statistical quantities of the system for a small real q.

scholarly journals Exact Solutions of the (2+1)-Dimensional Dirac Oscillator under a Magnetic Field in the Presence of a Minimal Length in the Non-commutative Phase Space

2015 ◽  
Vol 70 (8) ◽  
pp. 619-627 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Hassan Hassanabadi
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Phase Space ◽  
Hypergeometric Functions ◽  
Relativistic Quantum ◽  
Minimal Length ◽  
Wave Functions ◽  
Relativistic Quantum Mechanics ◽  
Two Dimensional ◽  
Dirac Oscillator

AbstractWe consider a two-dimensional Dirac oscillator in the presence of a magnetic field in non-commutative phase space in the framework of relativistic quantum mechanics with minimal length. The problem in question is identified with a Poschl–Teller potential. The eigenvalues are found, and the corresponding wave functions are calculated in terms of hypergeometric functions.

scholarly journals Thermal properties of a two-dimensional Duffin–Kemmer–Petiau oscillator under an external magnetic field in the presence of a minimal length

2020 ◽  
Vol 35 (33) ◽  
pp. 2050278
Author(s):  
H. Aounallah ◽  
B. C. Lütfüoğlu ◽  
J. Kříž
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Energy Eigenvalue ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Summation Formula ◽  
Minimal Length ◽  
Two Dimensional ◽  
Relativistic Limit ◽  
Ordinary Quantum

Generalized uncertainty principle puts forward the existence of the shortest distances and/or maximum momentum at the Planck scale for consideration. In this article, we investigate the solutions of a two-dimensional Duffin–Kemmer–Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) scale. First, we obtain the eigensolutions in ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of an ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions in the non-relativistic limit. We show that in the ordinary quantum mechanic limit, where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler–Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale.

Ordering Problems in Fermionic Relativistic Quantum Mechanics

1997 ◽  
Vol 12 (01) ◽  
pp. 243-248 ◽  
Author(s):  
Rodolfo P. Martínez Y Romero ◽  
Antonio Del Sol Mesa
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Typical Case ◽  
Relativistic Quantum Mechanics ◽  
Dirac Oscillator ◽  
Minimal Coupling ◽  
Relativistic Systems

We discuss the existence of ambiguities, or anomalies of fermionic nature as we call them, in the quantization of relativistic systems with odd Grassmann degrees of freedom. We propose in this work a way of avoiding such ambiguities in the case of relativistic quantum mechanics, by including the odd degrees of freedom into a generalization of the momentum, in a similar manner to the minimal coupling. We illustrate our results with some examples, including the Dirac oscillator as a typical case of the problems we are dealing with.

scholarly journals A family of analytically solvable Schrödinger equations related by Levi-Civita transformation

2019 ◽  
Vol 16 (3) ◽  
pp. 103
Author(s):  
Le Dai Nam ◽  
Phan Anh Luan ◽  
Luu Phong Su ◽  
Phan Ngoc Hung
Keyword(s):  
Exact Solution ◽  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Anharmonic Oscillator ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Schrödinger Equations ◽  
Two Dimensional ◽  
Spatial Transformations ◽  
Solvable Problems

Some two-dimensional problems in non-relativistic quantum mechanics can connect to each other by certain spatial transformations such as Levi-Civita transformation. This property allows forming a series of two-dimensional problems into an interrelated family. Starting from two related problems namely Coulomb plus harmonic oscillator and sextic double-well anharmonic oscillator potentials, such family is constructed via repeatedly applying Levi-Civita transformations. Obviously, this family contains various of exactly analytically solvable problems. The quasi-exact solution for each unknown member of this family is also obtained and systematically investigated.

scholarly journals The Statistical Properties of theq-Deformed Dirac Oscillator in One and Two Dimensions

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Dynamics ◽  
Relativistic Quantum ◽  
Small Deformation ◽  
Two Dimensions ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
One Dimensional ◽  
Pure Phase ◽  
The One

We study the behavior of the eigenvalues of the one and two dimensions ofq-deformed Dirac oscillator. The eigensolutions have been obtained by using a method based on theq-deformed creation and annihilation operators in both dimensions. For a two-dimensional case, we have used the complex formalism which reduced the problem to a problem of one-dimensional case. The influence of theq-numbers on the eigenvalues has been well analyzed. Also, the connection between theq-oscillator and a quantum optics is well established. Finally, for very small deformationη, we (i) showed the existence of well-knownq-deformed version of Zitterbewegung in relativistic quantum dynamics and (ii) calculated the partition function and all thermal quantities such as the free energy, total energy, entropy, and specific heat. The extension to the case of Graphene has been discussed only in the case of a pure phase (q=eiη).

scholarly journals Pseudoharmonic oscillator in quantum mechanics with a minimal length

2014 ◽  
Vol 29 (28) ◽  
pp. 1450143 ◽  
Author(s):  
Djamil Bouaziz ◽  
Abdelmalek Boukhellout
Keyword(s):  
Quantum Mechanics ◽  
Diatomic Molecules ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Relativistic Quantum Mechanics ◽  
Perturbative Approach ◽  
Minimal Length Scale ◽  
Pseudoharmonic Oscillator

The pseudoharmonic oscillator potential is studied in non-relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale, [Formula: see text]. By using a perturbative approach, we derive an analytical expression of the energy spectrum in the first-order of the minimal length parameter β. We investigate the effect of this fundamental length on the vibration–rotation energy levels of diatomic molecules through this potential function interaction. We explicitly show that the minimal length would have some physical importance in studying the spectra of diatomic molecules.

scholarly journals On the Relativistic Quantum Mechanics of a Particle in Space with Minimal Length

2012 ◽  
Vol 57 (9) ◽  
pp. 942
Author(s):  
Ch.M. Scherbakov
Keyword(s):  
Quantum Mechanics ◽  
Commutation Relation ◽  
Relativistic Quantum ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Group Symmetry ◽  
Relativistic Quantum Mechanics ◽  
Noncommutative Space ◽  
Quantum Mechanical

A noncommutative space and the deformed Heisenberg algebra [X,P] = iħ{1 – βP2}1/2 are investigated. The quantum mechanical structures underlying this commutation relation are studied. The rotational group symmetry is discussed in detail.

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