Bound-states of diatomic molecules in the Dirac equation with the q -deformed Morse potential

2011 ◽  
Vol 112 (4) ◽  
pp. 1029-1035 ◽  
Author(s):  
D. Agboola
Keyword(s):  
Dirac Equation ◽  
Morse Potential ◽  
Bound States ◽  
Diatomic Molecules

scholarly journals Comment on “Solutions of the Dirac equation with an improved expression of the Rosen–Morse potential energy model including Coulomb-like tensor interaction”

2019 ◽  
Vol 97 (10) ◽  
pp. 1167-1169
Author(s):  
S. Bouledjedj ◽  
A. Khodja ◽  
F. Benamira ◽  
L. Guechi
Keyword(s):  
Dirac Equation ◽  
Morse Potential ◽  
Bound States ◽  
Hypergeometric Functions ◽  
Energy Levels ◽  
Transcendental Equation ◽  
Tensor Interaction ◽  
Polynomial Method ◽  
Generalized Hypergeometric Functions ◽  
Spinor Wave

The Nikiforov–Uvarov polynomial method employed by Aguda (Can. J. Phys. 2013, 91: 689. doi: 10.1139/cjp-2013-0109 ) to solve the Dirac equation with an improved Rosen–Morse potential plus a Coulomb-like tensor potential is shown to be inappropriate because the conditions of its application are not fulfilled. We clarify the problem and construct the correct solutions in the spin and pseudospin symmetric regimes via the standard method of solving differential equations. For the bound states, we obtain the spinor wave functions in terms of the generalized hypergeometric functions 2F1(a, b, c; z) and in each regime we show that the energy levels are determined by the solutions of a transcendental equation that can be solved numerically.

Spin and pseudospin symmetries of the Dirac equation for the generalised Morse potential and a class of Yukawa potential

Pramana ◽  
2021 ◽  
Vol 95 (3) ◽  
Author(s):  
Obu J Abebe ◽  
Okoi P Obeten ◽  
Uduakobong S Okorie ◽  
Akpan N Ikot
Keyword(s):  
Dirac Equation ◽  
Morse Potential ◽  
Yukawa Potential

scholarly journals TOPOLOGICAL INSULATOR AND THE DIRAC EQUATION

SPIN ◽  
2011 ◽  
Vol 01 (01) ◽  
pp. 33-44 ◽  
Author(s):  
SHUN-QING SHEN ◽  
WEN-YU SHAN ◽  
HAI-ZHOU LU
Keyword(s):  
Dirac Equation ◽  
Topological Insulator ◽  
Bound States ◽  
Topological Insulators ◽  
Mass Term ◽  
Point Of View ◽  
Quadratic Term ◽  
General Description ◽  
Dirac Equations ◽  
Topological Quantum

We present a general description of topological insulators from the point of view of Dirac equations. The Z2 index for the Dirac equation is always zero, and thus the Dirac equation is topologically trivial. After the quadratic term in momentum is introduced to correct the mass term m or the band gap of the Dirac equation, i.e., m → m − Bp2, the Z2 index is modified as 1 for mB > 0 and 0 for mB < 0. For a fixed B there exists a topological quantum phase transition from a topologically trivial system to a nontrivial system when the sign of mass m changes. A series of solutions near the boundary in the modified Dirac equation is obtained, which is characteristic of topological insulator. From the solutions of the bound states and the Z2 index we establish a relation between the Dirac equation and topological insulators.

scholarly journals Exact Solutions of a Spatially Dependent Mass Dirac Equation for Coulomb Field plus Tensor Interaction via Laplace Transformation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
M. Eshghi ◽  
M. Hamzavi ◽  
S. M. Ikhdair
Keyword(s):  
Dirac Equation ◽  
Laplace Transformation ◽  
Bound States ◽  
Energy Eigenvalue ◽  
Coulomb Field ◽  
Transformation Method ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Dependent Mass ◽  
Laplace Transformation Method

The spatially dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction potential under the spin and pseudospin (p-spin) symmetric limits by using the Laplace transformation method (LTM). Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ. Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit and in the absence of tensor interaction (T=0).

scholarly journals Fermions in the Rindler spacetime

2019 ◽  
Vol 16 (09) ◽  
pp. 1950140 ◽  
Author(s):  
L. C. N. Santos ◽  
C. C. Barros
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Energy Spectrum ◽  
Dirac Equation ◽  
Reference Frame ◽  
Bound States ◽  
Liouville Problem ◽  
External Potential ◽  
Compact Expression ◽  
Sturm Liouville

In this paper, we study the Dirac equation in the Rindler spacetime. The solution of the wave equation in an accelerated reference frame is obtained. The differential equation associated to this wave equation is mapped into a Sturm–Liouville problem of a Schrödinger-like equation. We derive a compact expression for the energy spectrum associated with the Dirac equation in an accelerated reference. It is shown that the noninertial effect of the accelerated reference frame mimics an external potential in the Dirac equation and, moreover, allows the formation of bound states.

scholarly journals Investigation of DNA denaturation from generalized Morse potential

2018 ◽  
Vol 3 (2) ◽  
Author(s):  
R. El Kinani ◽  
H. Kaidi ◽  
M. Benhamou
Keyword(s):  
Morse Potential ◽  
Bound States ◽  
Analytical Study ◽  
Free Energy Density ◽  
Exact Expression ◽  
Dna Denaturation ◽  
Denaturation Temperature ◽  
Finite Distance ◽  
The Mean ◽  
Generalized Morse Potential

In this paper, we present a non-linear model for the study of DNA denaturation transition. To this end, we assume that the double-strands DNA interact via a realistic generalized Morse potential that reproduces well the features of the real interaction. Using the Transfer Matrix Method, based on the resolution of a Schrödinger equation, we first determine exactly their solution, which are found to be bound states. Second, from an exact expression of the ground state, we compute the denaturation temperature and the free energy density, in terms of the parameters of the potential.Then, we calculate the contact probability, which is the probability to find the double-strands at a (finite) distance apart, from which we determine the behaviour of the mean-distance between DNA-strands.The main conclusion is that, the present analytical study reveals that the generalized Morse potential is a good candidate for the study of DNA denaturation

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