Relativistic symmetries in trigonometric Poschl-Teller potential plus tensor interaction

TL;DR

This paper solves the Dirac equation with a trigonometric Poschl-Teller potential and tensor interaction, analyzing relativistic symmetries and providing numerical energy spectra for different quantum states.

Contribution

It introduces an approximation scheme for centrifugal terms and applies the asymptotic iteration method to find relativistic bound states with tensor interactions.

Findings

Relativistic energy eigenvalues are obtained for various potentials and quantum numbers.

The effect of tensor coupling on energy levels is numerically analyzed.

Non-relativistic limits of the solutions are also derived.

Abstract

The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Poschl-Teller (tPT) potential including a Coulomb-like tensor interaction with arbitrary spin-orbit quantum number $\kappa$ using an approximation scheme to substitute the centrifugal terms k(k+1)/r^2. In view of spin and pseudo-spin (p-spin) symmetries, the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method (AIM). We present numerical results in the absence and presence of tensor coupling $A$ and for various values of spin and p-spin constants and quantum numbers n and k. The non-relativistic limit is also obtained.