Exact Solutions of the Modified Kratzer Potential Plus Ring-Shaped Potential in the D-Dimensional Schrödinger Equation by the Nikiforov–uvarov Method

Abstract

We present analytically the exact energy bound-states solutions of the Schrödinger equation in D-dimensions for a recently proposed modified Kratzer potential plus ring-shaped potential by means of the conventional Nikiforov-Uvarov method. We give a clear recipe of how to obtain an explicit solution to the wave functions in terms of orthogonal polynomials. The results obtained in this work are more general and true for any dimension which can be reduced to the standard forms in three-dimensions given by other works.

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

“…In this case, we have the spin-orbit coupling term κ(κ + 1)/ 2 = 0 and also the corresponding approximation to it in Eq. (22). The corresponding energy equation reduces to the -states (κ = −1), i.e.,…”

“…However, for -waves, we remark that the problem can be solved exactly and the solution is valid for any deformation parameter We define the following new dimensionless parameter, z( ) = − −α ∈ [− R 0 / 0], which maintains the finiteness of the transformed wave functions on the boundary conditions Thus using Eqs. (22) and (23) (…”

Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods–Saxon Potential Plus Double Ring-Shaped Potential

“…The relations between these cartesian coordinates and the hyperspherical coordinates r and θ j in D-dimensional space are defined by [37][38][39][40][41][42]:…”

“…The Schrödinger equation has been investigated for several potentials as the Woods-Saxon potential [18][19][20], harmonic oscillator potential [21], Hulthén potential [22][23][24][25], Kratzer potential [26], generalized q-deformed Morse potential [27], modifed Woods-Saxon potential [28], Makarov potential [29], deformed Woods-Saxon Potential [30], Pseudoharmonic potential [31,32], Yukawa potential [33,34] and Eckart potential [35,36]. Very recently, the Schrödinger equation in generalized D dimensions for different potentials is getting more attention with the aim of generalizing the solutions to multidimensional space for many potentials [37][38][39][40][41][42][43][44][45][46].…”

Relativistic Treatment of Massive Klein-Gordon Particle by Modified Generalized Hulthen Potential

“…When a particle is in a strong potential field, the relativistic effect must be considered, which gives the correction for non relativistic quantum mechanics [14]. In solving non relativistic or relativistic wave equation whether for central or non central potential, various methods are used such as Asymptotic iteration method (AIM) [15], Super symmetric quantum mechanics (SUSYQM) [16] shifted N 1 expansion [17], factorization [18], Nikiforov-Uvarov (NU) *To whom correspondence should be addressed: E-mail: antiacauchy@yahoo.com, akaninyeneantia@uniuyo.edu.ng method [19] etc.…”