Solution of the Dirac equation with position-dependent mass in the Coulomb field

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).

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SOLUTION OF THE DIRAC EQUATION WITH POSITION-DEPENDENT MASS IN A COULOMB AND SCALAR FIELDS IN A CONICAL SPACETIME

Modern Physics Letters A ◽

10.1142/s021773231350137x ◽

2013 ◽

Vol 28 (31) ◽

pp. 1350137 ◽

Cited By ~ 13

Author(s):

GEUSA DE A. MARQUES ◽

V. B. BEZERRA ◽

SHI-HAI DONG

Keyword(s):

Dirac Equation ◽

Cosmic String ◽

Relativistic Particle ◽

Energy Levels ◽

Scalar Potential ◽

Scalar Fields ◽

The Self ◽

Dependent Mass ◽

Scalar Potentials ◽

Position Dependent Mass

We consider the problem of a relativistic particle with position-dependent mass in the presence of a Coulomb and a scalar potentials in the background spacetime generated by a cosmic string. The scalar potential arises from the self-interaction potential which is induced by the conical geometry of the spacetime under consideration. We find the solution of the corresponding Dirac equation and determine the energy spectrum of the particle. The behavior of the energy levels on the parameters associated with the presence of the cosmic string and with the fact that the mass of the particle depends on its position is also analyzed.

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Bound state of solution of Dirac-Coulomb problem with spatially dependent mass

Open Physics ◽

10.2478/s11534-014-0448-9 ◽

2014 ◽

Vol 12 (4) ◽

Author(s):

Eser Olğar ◽

Hayder Dhahir ◽

Haydar Mutaf

Keyword(s):

Dirac Equation ◽

Coulomb Potential ◽

Mass Function ◽

Bound State ◽

Asymptotic Iteration Method ◽

Bound State Solution ◽

Function Generator ◽

Dependent Mass ◽

And Function ◽

Position Dependent Mass

AbstractThe bound state solution of Coulomb Potential in the Dirac equation is calculated for a position dependent mass function M(r) within the framework of the asymptotic iteration method (AIM). The eigenfunctions are derived in terms of hypergeometric function and function generator equations of AIM.

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Approximation solution of the Dirac equation with position-dependent mass for the generalized Hulthén potential

Physics Letters A ◽

10.1016/j.physleta.2005.12.039 ◽

2006 ◽

Vol 352 (6) ◽

pp. 478-483 ◽

Cited By ~ 36

Author(s):

Xiao-Long Peng ◽

Jian-Yi Liu ◽

Chun-Sheng Jia

Keyword(s):

Dirac Equation ◽

Approximation Solution ◽

Hulthén Potential ◽

Hulthen Potential ◽

Dependent Mass ◽

Position Dependent Mass

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Position-dependent mass Dirac equation and local Fermi velocity

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8121/ac3ce0 ◽

2021 ◽

Author(s):

Rahul Ghosh

Keyword(s):

Dirac Equation ◽

Free Particle ◽

Quadratic Functional ◽

Fermi Velocity ◽

New Approach ◽

Coupled Equations ◽

The One ◽

Dependent Mass ◽

Local Variable ◽

Position Dependent Mass

Abstract We present a new approach to study the one-dimensional Dirac equation in the background of a position-dependent mass m. Taking the Fermi velocity vf to be a local variable, we explore the resulting structure of the coupled equations and arrive at an interesting constraint of m turning out to be the inverse square of vf. We address several solvable systems that include the free particle, shifted harmonic oscillator, Coulomb and nonpolynomial potentials. In particular, in the supersymmetric quantum mechanics context, the upper partner of the effective potential yields a new form for an inverse quadratic functional choice of the Fermi velocity.

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