Solution of Spinless Salpeter Equation with Generalized Hulthén Potential Using SUSYQM

Abstract

The spinless Salpeter equation (SSE) may be considered as a standard approximation to the Bethe Salpeter formalism, neglecting the spin degree freedom [1]. The Bethe Salpeter equation is the semirelativistic equation that describes the bound states of a two-body quantum eld system in a relativistic covariant formalism [2]. In the recent times, there have been increasing interests in nding the analytical solutions of wave equations in relativistic and nonrelativistic quantum mechanics such as Schrodinger, Klein Gordon, Dirac, Du n Kemmer Petiau (DKP) and spinless Bethe Salpeter equations with di erent potential models [3 10]. The nonlocal nature of the Hamiltonian resulting from this approximation renders di culty in obtaining SSE solutions [11]. The SSE is a generalization of Schrodinger equation in the quantum relativistic regime [12]. Consequently, many authors have resorted to approximate techniques to deal with the problems arising from the SSE [13]. In the recent times, many authors has investigated the SSE for various potential models. Hassanabadi et al. [14] studied the SSE with hyperbolic potential via the SUSYQM formalism. Zarrinkamar et al. [15] studied the two-body Sapelter equation with exponential potential using SUSYQM method. In this work, we used supersymmetric quantum mechanics (SUSYQM) [16 18] to solve SSE with generalized Hulthen potential. The Hulthen potential is a shortrange potential in physics which behaves like a Coulomb potential for a small values of r and decreases exponentially for a larger values of r [19]. The Hulthen potential is very important in atom and molecule elds [20]. This potential has been used to explain the electronic properties of F-color centre in alkali halides [21].