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

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 V 0 and W , the radial n r and l orbital quantum numbers and parameters D, a, R 0 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 F e 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.

Generalised tanh-shaped hyperbolic potential: Klein–Gordon equation's bound state solution

“…In principle, the exponential potential models always draw considerable attention and are widely used in various physical systems, including quantum cosmology, nuclear physics, molecular physics, elementary particle physics, and condensed matter physics [19][20][21][22][23][24][25][26][27][28][29]. Up to now, many exponential-type potentials, including the Morse [30,31], Hulthén [32][33][34][35][36][37][38], Woods-Saxon [27,[39][40][41][42][43], Rosen-Morse [44][45][46][47][48], Eckart-type [49][50][51], Manning-Rosen [52][53][54], Deng-Fan [55,56], Pöschl-Teller like [57], Mathieu [58], sine-type hyperbolic [59] and Schiöberg [60][61][62][63] potentials have been investigated, and some analytical bound state solutions were obtained using an approximation for these models ...…”

Approximate analytical solutions of the Schrodinger equation in central potential field

“…Bound state solutions of the Schrödinger equation for a quantum system interacting with spherical symmetric potential models are among the most important in various fields of physics. The l-state solutions of the non-relativistic wave equation for exponential potentials especially are of great interest in literature [1,2,3,4]. Under consideration of this problem, it cannot be possible to obtain analytical solutions without approximations.…”

Analytical Bound State Solutions of the Klein-Fock-Gordon Equation for the Sum of Hulthén and Yukawa Potential within SUSY Quantum Mechanics

“…Unfortunately, for arbitrary l states (l ≠ 0), the KFG equation cannot get an exact solution with these potentials due to the centrifugal term of potentials. The numerous research works reveal the SUSY QM method's power and simplicity in solving wave equations of the central and noncentral potentials for arbitrary l states [42][43][44][45][46][47][48][49].…”