Exact Solutions of the Klein-Gordon Equation for the Rosen-Morse type Potentials via Nikiforov-Uvarov Method

TL;DR

This paper derives exact solutions for the Klein-Gordon equation with Rosen-Morse type potentials using the Nikiforov-Uvarov method, including wave-functions, energy levels, and PT-symmetry considerations.

Contribution

It applies the Nikiforov-Uvarov method to obtain exact bound state solutions for Rosen-Morse type potentials in the Klein-Gordon framework, extending previous results.

Findings

Wave-functions and energy equations derived for Rosen-Morse potentials.

Results reduce to Rosen-Morse and Eckart potentials in special cases.

PT-symmetry properties of these potentials are analyzed.

Abstract

The exact solutions of the one-dimensional Klein-Gordon equation for the Rosen-Morse type potential with equal scalar and vector potentials are presented. First we briefly review Nikiforov-Uvarov mathematical method. Using this method, wave-functions and corresponding exact energy equation are obtained for the s-wave bound state. It has been shown that the results for Rosen-Morse type potentials reduce to standard Rosen-Morse well and Eckart potentials in the special case. The PT-symmetry for these potentials is also considered.