In this work, the three dimensional Woods-Saxon potential is studied within the context of Supersymmetry Quantum Mechanics. We have applied the SUSY method by using the Pekeris approximation to the centrifugal potential l = 0 states. By application of this method, it is possible to solve the Schrödinger equation for this potential. We obtain exactly bound state spectrum and wave function of Woods-Saxon potential for nonzero angular momentum. Hamiltonian hierarchy method and the shape invariance property are used in the calculations.
In this paper, by applying the Pekeris approximation and in the frame of Supersymmetric Quantum Mechanics (SUSYQM), the semi-relativistic solutions of the two-body spinless Salpeter equation are obtained analytically. For an interaction of nuclear form, we obtain the approximate bound-state energy eigenvalues and the corresponding wave functions using the shape invariance concept. The solutions are reported for any l state and some energy eigenvalues are given. These results are useful in elementary-particle physics and nuclear physics to obtain the bound states spectra of relativistic systems such as fermion–antifermion systems.
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