Solutions of D-dimensional Schrodinger equation for Woods–Saxon potential with spin–orbit, coulomb and centrifugal terms through a new hybrid numerical fitting Nikiforov–Uvarov method

Abstract

Solution of the radial Schrodinger equation for the Woods-Saxon potential together with spin-orbit interaction, coulomb and centrifugal terms by using usual Nikiforov-Uvarov (NU) method is not possible. Here, we have presented a new NU procedure with which we are able to solve this Schrodinger equation and any other onedimensional ones with any shape of the potential profile.

An Approximate Analytical Solution of the Nonlinear Schrödinger Equation with Harmonic Oscillator Using Homotopy Perturbation Method and Laplace-Adomian Decomposition Method

“…where ∈ [0, 1] is a parameter which increases from 0 to 1, R represents all real numbers, and Ψ 0 is an initial approximate solution of (10), which satisfies the boundary conditions (11). Clearly, from (13) we have…”

“…In recent years, a considerable amount of research focused on finding analytical solution to the Schrödinger equations using various methods, among which are Adomian Decomposition Method [3][4][5][6][7][8], Elzaki decomposition method [9], Variation Iteration method [10], Nikiforod-Uvarov (NV) method [11], and Homotopy Perturbation Method [3,4,[12][13][14][15][16]. Additionally, Borhanifar [17] solved the nonlinear Schrödinger and coupled Schrödinger equations with a differential transformation method.…”

A comparative interpretation of the thermodynamic functions of a relativistic bound state problem proposed with an attractive or a repulsive surface effect

“…Since then, the Woods-Saxon potential (WSP) energy is used in huge amount of applications in various branches of physics. For instance, in nuclear physics some of recent studies can be given in [3][4][5][6][7][8][9][10][11][12][13][14][15] in addition to two reports [16,17], in atomic and molecular physics [18][19][20][21], in non relativistic [22][23][24][25][26] and in relativistic quantum mechanics [27][28][29][30][31][32][33][34].…”

Properties of an α Particle in a Bohrium 270 Nucleus under the Generalized Symmetric Woods-Saxon Potential

“…The Woods-Saxon Potential (WSP) [9] has been widely used in many areas of physics such as nuclear physics [9][10][11][12][13][14][15][16], atom-molecule physics [16,17], relativistic [18][19][20][21][22][23][24][25][26] and non-relativistic [27][28][29][30] problems. In order to take the effects such as non-zero l, spin-orbit coupling, large force suffered by nucleons near the surface of a nucleus, additional terms to WSP have been introduced to form various types of Generalized Symmetric Woods-Saxon Potential (GSWSP) [31][32][33][34][35][36][37][38][39][40][41][42][43].…”