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Journal of Physics A Mathematical and General

The Klein–Gordon equation of generalized Hulthén potential in complex quantum mechanics

Mehmet Şimşek, Harun Eğrifes

Published Mar 29, 2004• 143 citations
Publisher

Abstract

We have investigated the reality of exact bound states of complex and/or PT-symmetric non-Hermitian exponential-type generalized Hulthen potential. The Klein–Gordon equation has been solved by using the Nikiforov–Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type. In many cases of interest, negative and positive energy states have been discussed for different types of complex potentials.

DOI
10.1088/0305-4470/37/15/007

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We have investigated the reality of exact bound states of complex and/or PT-symmetric non-Hermitian exponential-type generalized Hulthen potential. The Klein–Gordon equation has been solved by using the Nikiforov–Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type. In many cases of interest, negative and positive energy states have been discussed for different types of complex potentials.
BOUND-STATES OF A SEMI-RELATIVISTIC EQUATION FOR THE PT{\cal PT}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.
In this study, we focus on investigating the exact relativistic bound-state spectra for supersymmetric, PT -supersymmetric and non -Hermitian versions of the q -deformed parameter Hulthén potential. The Hamiltonian hierarchy mechanism, namely the factorization method , is adopted within the framework of SUSYQM. This algebraic approach is used in solving 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 ro-vibrational states, and optical spectra characteristics of semiconductor devices with regard to the lattice dynamics. They are also employed to construct the broken or unbroken case of the supersymmetric particle model concerning the interaction between the elementary particles.