Solutions of Woods—Saxon Potential with Spin-Orbit and Centrifugal Terms through Nikiforov—Uvarov Method

Abstract

In this study, the analytical solutions of the radial Schrödinger equation for the central Woods—Saxon potential together with spin-orbit interaction and centrifugal terms have been derived by using Nikiforov-Uvarov method. The energy eigenvalues and corresponding eigenfunctions of nucleons have been obtained for various values of n, l, and j quantum numbers. The obtained results using this method are in satisfactory agreement with available data in the special case.

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

“…However, some theoretical groups have tried to solve these Schrodinger equations analytically. For example, Pahlavani et al have solved the Schrodinger equation including Woods-Saxon potential with spin-orbit and centrifugal terms by Nikiforov-Uvarov method [3]. They did not include the coulomb term to their calculations.…”

“…Here, we have extended the Ref. [3] by adding a coulomb term to its potential. Adding this potential enhances the difficulty of the problem very much.…”

“…Thus, we had to change the transformations and other formulas of the Ref. [3] to be able to solve the Schrodinger equation. Finally, energy eigenvalues and corresponding eigenfunctions obtained.…”

Axially symmetrical molecules in electric and magnetic fields: energy spectrum and selection rules

“…These models cover a very wide area of physical problems, such as molecular vibrations, motion of an electron in the field of crystalline lattice in metals or semiconductors, quantum dots confined in parabolic potential, the impact and probable hazards caused by electromagnetic fields on living organisms etc [1][2][3][4][5][6][7][8][9][10]. Various quantum mechanical models for analytical modeling of multi-dimensional atomic and molecular vibrations have been developed and different methods of solving equations have been used [4][5][6][11][12][13][14][15]. In most cases, the actual multi-dimensional problem is observed as a system of one-dimensional problems, in order to reduce the computational effort required to solve the Schrödinger equation in 2 or 3 dimensions.…”

Spinless Particles Subject to Unequal Scalar-Vector Nuclear Woods– Saxon Potentials in Arbitrary Dimensions

“…Ikot and Akpan investigated the energy spectra and the wave function depending on the c-factor for a more general WoodsSaxon potential with an arbitrary l-state [12]. Very recently, Pahlavani and Alavi derived the analytical solutions of the radial Schrödinger equation for the central Woods-Saxon potential together with spin-orbit interaction and centrifugal terms by using the NikiforovUvarov (NU) method [13].…”