The Dirac equation in (1+1) dimension with the complex vector potential coupling that leads to an effective Hulthen potential model is solved. Polynomial solutions are obtained using the method of Nikiforov-Uvarov. Energy spectrum and corresponding wave-functions are obtained.
BOUND-STATES OF A SEMI-RELATIVISTIC EQUATION FOR THE PT-SYMMETRIC GENERALIZED HULTHÉN POTENTIAL BY THE NIKIFOROV–UVAROV METHOD
The one-dimensional semi-relativistic equation has been solved for the [Formula: see text]-symmetric generalized Hulthén potential. The Nikiforov–Uvarov (NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type, is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have investigated the positive and negative exact bound states of the s-states for different types of complex generalized Hulthén potentials.