scholarly journals Nonperturbative effects of the minimal length uncertainty on the relativistic quantum mechanics

2012 ◽  
Vol 710 (3) ◽  
pp. 478-485 ◽  
Author(s):  
Pouria Pedram
Keyword(s):  
Quantum Mechanics ◽  
Nonperturbative Effects ◽  
Relativistic Quantum ◽  
Minimal Length ◽  
Relativistic Quantum Mechanics

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.

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.

Stochastic microcausality in relativistic quantum mechanics

1984 ◽  
Vol 14 (9) ◽  
pp. 883-906 ◽  
Author(s):  
D. P. Greenwood ◽  
E. Prugovečki
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics

Relativistic Multiple Scattering Theory

1991 ◽  
Vol 253 ◽  
Author(s):  
B. L. Gyorffy
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Schr6dinger Equation ◽  
Relativistic Effects ◽  
Relativistic Quantum Mechanics ◽  
Absolute Minimum ◽  
Crystalline Anisotropy ◽  
Symmetry Properties ◽  
Finite Set

The symmetry properties of the Dirac equation, which describes electrons in relativistic quantum mechanics, is rather different from that of the corresponding Schr6dinger equation. Consequently, even when the velocity of light, c, is much larger than the velocity of an electron Vk, with wave vector, k, relativistic effects may be important. For instance, while the exchange interaction is isotropic in non-relativistic quantum mechanics the coupling between spin and orbital degrees of freedom in relativistic quantum mechanics implies that the band structure of a spin polarized metal depends on the orientation of its magnetization with respect to the crystal axis. As a consequence there is a finite set of degenerate directions for which the total energy of the electrons is an absolute minimum. Evidently, the above effect is the principle mechanism of the magneto crystalline anisotropy [1]. The following session will focus on this and other qualitatively new relativistic effects, such as dichroism at x-ray frequencies [2] or Fano effects in photo-emission from non-polarized solids [3].

scholarly journals PROBABILITY IN RELATIVISTIC QUANTUM MECHANICS AND FOLIATION OF SPACE–TIME

2007 ◽  
Vol 22 (32) ◽  
pp. 6243-6251 ◽  
Author(s):  
HRVOJE NIKOLIĆ
Keyword(s):  
Quantum Mechanics ◽  
Wave Equations ◽  
Integral Curve ◽  
Relativistic Quantum ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Relativistic Wave ◽  
Probability Densities ◽  
The Many ◽  
Conserved Currents

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of space–time must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.

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