A Novel SUSY Energy Bound States Treatment of the Klein-Gordon Equation with PT-Supersymmetric and q-Deformed Hulthen Potential

TL;DR

This paper analytically solves the Klein-Gordon equation for a q-deformed Hulthen potential within SUSYQM, exploring relativistic bound states in PT-symmetric and non-Hermitian contexts, with potential applications in molecular and semiconductor physics.

Contribution

It introduces an algebraic method to find exact bound state spectra for a novel class of potentials in relativistic quantum mechanics, extending SUSYQM techniques to q-deformed and PT-symmetric cases.

Findings

Analytical expressions for bound state energies obtained.

Results are consistent for specific q-values.

Potential applications in molecular and semiconductor physics.

Abstract

In this study, we focus on investigating the exact relativistic bound state spectra for supersymmetric, PT-supersymmetric and non-Hermitian versions of q-deformed parameter Hulthen potential. The Hamiltonian hierarchy mechanism, namely the factorization method, is adopted within the framework of SUSYQM. This algebraic approach is used in solving of the Klein-Gordon equation with the potential cases. The results obtained analytically by executing the straightforward calculations are in consistent forms for certain values of q. Achieving the results may have a particular interest for such applications. That is, they can be involved in determining the quantum structural properties of molecules for rovibrational states, and optical spectra characteristics of semiconductor devices with regard to the lattice dynamics [62-64]. They are also employed to construct broken or unbroken case of supersymmetric particle model concerning the interaction between the elementary particles [65].