The bound state solutions of the $D$-dimensional Schrödinger equation for the Woods-Saxon potential

Abstract

In this work, the analytical solutions of the $D$-dimensional Schrödinger equation are studied in great detail for the Wood-Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any angular momentum case within the context of the Nikiforov-Uvarov (NU) and Supersymmetric quantum mechanics (SUSYQM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformed each other is demonstrated. In addition, a finite number energy spectrum depending on the depth of the potential $V_0$, the radial $n_r$ and orbital $l$ quantum numbers and parameters $D,a,R_0$ are defined as well.

arXiv comment26 pages, 2 tables, 2 figures. arXiv admin note: substantial text overlap with arXiv:1711.10322, arXiv:1111.4734, arXiv:0905.2731, arXiv:0912.3890; text overlap with arXiv:hep-th/9405029 by other authors

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Cited by in corpus (4)

• Bound State Solution of the Klein-Fock-Gordon equation with the Hulthén plus a Ring-Shaped like potential within SUSY quantum mechanics
• Bound states of the $D$-dimensional Schrödinger equation for the generalized Woods-Saxon potential
• PDM-charged particles in PD-magnetic plus Aharonov-Bohm flux fields: unconfined "almost-quasi-free" and confined in a Yukawa plus Kratzer exact solvability
• Quantum Gravity Corrections to the Mean Field Theory of Nucleons