Bound states of the D-dimensional Schrödinger equation for the generalized Woods-Saxon potential

2017/11/24 by V. H. Badalov, Badalov, V. H., Baris, B. +2
Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Nuclear Theory (nucl-th) #Nuclear physics research studies #Quantum Mechanics and Non-Hermitian Physics #Quantum, superfluid, helium dynamics

paper · pdf · doi:10.48550/arxiv.1711.10322

openalex publication_date 2017/11/24 · openalex created_date 2017/12/04 · openalex updated_date 2026/08/01

Abstract

In this paper, the approximate analitical solutions of the hyper-radial Schrödinger equation are obtained for the generalized Wood-Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy eigenvalues and corresponding hyper-radial wave functions are found for any angular momentum case via the Nikiforov-Uvarov (NU) and Supersymmetric quantum mechanics (SUSY QM) methods. Hence, the same expressions are obtained for the energy eigenvalues, and the expression of hyper-radial wave functions transformed each other is shown owing to these methods. Furthermore, a finite number energy spectrum depending on the depths of the potential well V₀ and W, the radial n_r and l orbital quantum numbers and parameters D,a,R₀ are also identified in detail. Finally, the bound state energies and the corresponding normalized hyper-radial wave functions for the neutron system of the a ⁵⁶ Fe nucleus are calculated in D=2 and D=3, as well as the energy spectrum expressions of other highest dimensions are identified by using the energy spectrum of D=2 and D=3.

Related

• Analytical solutions of the D-dimensional Schrödinger equation with the Woods-Saxon potential for arbitrary l state
• Bound State Solutions of Schrödinger Equation for a more general Woods-Saxon Potential with Arbitrary l - state
• Numerical solution of the Schrodinger equation for types of Woods-Saxon potential
• Deformed Woods-Saxon Potential in the Frame of Supersymmetric Quantum Mechanics for Any l-State
• Resonance and virtual bound state solutions of the radial Schrödinger equation