Particle resonance in the (1+1)-dimensional Dirac equation with kink-like vector potential and delta interaction

TL;DR

This paper investigates the energy spectrum and wave functions of spin-fermions in a (1+1)-dimensional Dirac equation with kink-like vector potential and delta interaction, using the Nikiforov-Uvarov method.

Contribution

It provides analytical solutions for the Dirac equation with kink-like potential and delta interaction, extending previous models with exact energy eigenvalues and wave functions.

Findings

Derived energy eigenvalues in terms of Jacobi polynomials

Obtained normalized wave functions for different spatial regions

Extended the solution method to include delta interactions

Abstract

The relativistic problem of spin- fermions subject to vector hyperbolic (kink-like) potential tanh (kx) is investigated by using the parametric Nikiforov-Uvarov method. The energy eigenvalue equation and the corresponding normalized wave functions are obtained in terms of the Jacobi polynomials for x>0 and x<0 cases.