Solution of Effective-Mass Dirac Equation with Scalar-Vector and Pseudoscalar Terms for Generalized Hulthén Potential

Altuğ Arda

doi:10.1155/2017/6340409

Abstract

We find the exact bound state solutions and normalization constant for the Dirac equation with scalar-vector-pseudoscalar interaction terms for the generalized Hulthén potential in the case where we have a particular mass functionm(x). We also search the solutions for the constant mass where the obtained results correspond to the ones when the Dirac equation has spin and pseudospin symmetry, respectively. After giving the obtained results for the nonrelativistic case, we search then the energy spectra and corresponding upper and lower components of Dirac spinor for the case of PT-symmetric forms of the present potential.

Highlights

The Hulthen potential [1] is one of the best known potentials in physics, as a short-range potential [2]
We extend the search including the solutions of the Dirac equation having a pseudoscalar interaction term, as in [22,23,24,25], for the qparameter Hulthen potential within the position-dependent mass (PDM) formalism
We have analyzed the analytical solutions of the Dirac equation with scalar-vector-pseudoscalar generalized Hulthen potential in 1 + 1 dimension within the position-dependent mass formalism

Summary

Introduction

The Hulthen potential [1] is one of the best known potentials in physics, as a short-range potential [2]. We search the bound state solutions of the generalized Hulthen potential which can be written in a complex form identifying the PT-symmetric case in a closed form for the case where the mass depends on spatial coordinate and extend the Dirac equation including the scalar, vector, and pseudoscalar interaction terms to this case. We extend the search including the solutions of the Dirac equation having a pseudoscalar interaction term, as in [22,23,24,25], for the qparameter Hulthen potential within the position-dependent mass (PDM) formalism This formalism gives an opportunity such as writing the analytical results for the case where the mass is constant. We find the appropriate mass function by using the equalities, and we write the bound state solutions with the corresponding normalized wave functions

Bound States for Generalized Hulthén Potential

Bound States for PT-Symmetric Forms

Solutions for Specific q-Values

Conclusions