Eigen solutions of the Schrodinger equation with variable mass under the influence of the linear combination of modified Woods–Saxon and Eckart potentials in toroidal coordinate

Abstract

The solutions of the Schrodinger equation was investigated in space-times with nonspherical topology in the presence of the linear combination of modified Woods–Saxon and Eckart potentials. The variable mass and Supersymmetric Quantum Mechanics method were used to solve the Schrodinger equation in toroidal coordinate. This solution was used to obtain the nonrelativistic energy eigenvalue and the wave function of the system. Using the proper super potential to deal with the hyperbolic form of the effective potential, the Schrodinger equation in the radial direction part was solved analytically for modified Woods–Saxon plus Eckart potentials. The energy eigenvalue and the un-normalised ground state wave function equations were obtained. The results showed that the energy value depends on the quantum number, the parameters of potentials, and variable separation constants.