Bound state solution and thermodynamic properties of the screened cosine Kratzer potential under influence of the magnetic field and Aharanov–Bohm flux field

Abstract

In this article, approximate analytical bound state solutions of the Schrödinger equation in two-dimensional space for screened cosine Kratzer potential (SCKP) under the influence of the magnetic field and Aharanov–Bohm flux field have been investigated. We obtained energy eigenvalues and wave functions for SCKP with external fields (magnetic field and Aharanov–Bohm flux field) via parametric Nikiforov–Uvarov (pNU) method using the approximation method suggested by Greene–Aldrich for handling centrifugal barriers. We deduced energy eigenvalues for screened Kratzer potential (SKP) and Hellmann potential (HP) from the obtained energy spectrum of SCKP with an external field. We extended our results in D dimensions for Hellmann potential in the absence of external fields. Thermodynamic properties such as partition function Z(B→,ΦAB,β), mean energy U(B→,ΦAB,β), mean free energy F(B→,ΦAB,β), entropy S(B→,ΦAB,β), specific heat capacity Cs(B→,ΦAB,β), magnetization at finite temperature (B→,ΦAB,β) and magnetic susceptibility χm(B→,ΦAB,β) at finite temperature are presented. The obtained numerical resultsfor SKP and Hellmann potential are in very good agreementwith numerical results available in the literature with and without external fields respectively.