Exact solution of Schrödinger equation with deformed ring-shaped potential

Abstract

Exact solution of the Schrödinger equation with deformed ring shaped potential is obtained in the parabolic and spherical coordinates. The Nikiforov-Uvarov method is used in the solution. Eigenfunctions and corresponding energy eigenvalues are calculated analytically. The agreement of our results is good.

Exact Bound State Solutions of the Schrödinger Equation for Noncentral Potential via the Nikiforov-Uvarov Method

“…These are also applicable to the scattering and condensed matter processes [28][29][30][31]. There have been many studies involving the potentials by using the well-known techniques, i.e., group theoretical manner [12,[32][33][34], supersymmetric formalism [35][36][37][38][39][40][41][42], path integral method [43][44][45][46][47][48][49][50] and other algebraic approaches [51][52][53][54][55][56][57][58][59][60].…”

Novel bound states treatment of the two dimensional Schrödinger equation with pseudocentral potentials plus multiparameter noncentral potential

“…One of our basic interests in this step is to show and present how to get the energy eigenvalue results for the radial-dependent equations (8) and (9) with the potential functions (3) and (4) respectively by employing the analogy procedure. It is obvious that the equation (38) and its converted equation (50) given as [48] are identical form to the equation (8). Accordingly, it should also admit to be similar form solutions.…”

“…Recently, much considerable effort for variety forms of NCPs has been expanded on the solutions of Schrödinger, Dirac and Klein-Gordon equations. The Feynman's path integral treatment [26][27][28][29][30] and the Green's function technique [31,32], the (Lie) algebraic/group theoretical approach [33][34][35][36], nonbijective canonical transformation [3,37], supersymmetric (SUSY) quantum mechanical formalism [38][39][40][41][42][43][44][45][46] and the NU-analytic method [47][48][49][50][51][52][53][54][55][56][57][58] as well as the applications for both relativistic [59][60][61][62][63][64][65][66][67][68][69][70][71] and other nonrelativistic…”

Analytical Solution of the Schrödinger Equation for Makarov Potential with any ℓ Angular Momentum

“…The ring shaped Hartmann potential, which includes attractive Coulomb and a repulsive inverse square potential, is performed by using several methods both the non-relativistic case [3,4,[19][20][21][22] and the relativistic case [23][24][25].…”