Dirac Equation with Spin Symmetry for the Modified P\"oschl-Teller Potential in $D$-dimensions

TL;DR

This paper solves the Dirac equation with spin symmetry for the modified P"oschl-Teller potential in D-dimensions, deriving energy spectra and wavefunctions using the Nikiforov-Uvarov method, revealing positive-energy bound states and their dependence on dimension and potential parameters.

Contribution

It provides analytical solutions for the Dirac equation with a specific potential in higher dimensions, including energy spectra and wavefunctions, under spin symmetry.

Findings

Bound states only have positive energies.

Energy levels increase with dimension and potential range parameter.

Wavefunctions expressed in terms of Jacobi polynomials.

Abstract

We present solutions of the Dirac equation with spin symmetry for vector and scalar modified P\"oschl-Teller potential within framework of an approximation of the centrifugal term. The relativistic energy spectrum is obtained using the Nikiforov-Uvarov method and the two-component spinor wavefunctions are obtain are in terms of the Jacobi polynomials. It is found that there exist only positive-energy states for bound states under spin symmetry, and the energy levels increase with the dimension and the potential range parameter $\alpha$.