Exact solution of the Schrödinger equation for the modified Kratzer potential plus a ring-shaped potential by the Nikiforov–Uvarov method

Abstract

We propose a new exactly solvable potential which consists of the modified Kratzer potential plus a new ring-shaped potential βctg 2 θ/r 2 . The exact solutions of the bound states of the Schrödinger equation for this potential are presented analytically by using the Nikiforov-Uvarov method, which is based on solving the second-order linear differential equation by reducing to a generalized equation of hypergeometric type. The wavefunctions of the radial and angular parts are taken on the form of the generalized Laguerre polynomials and the total energy of the system is different from the modified Kratzer potential because of the contribution of the angular part.

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

“…Besides, considerable efforts have been made to obtain analytical solutions of the Schrödinger equation or the Klein-Gordon equation with ring-shaped potentials [2,[59][60][61][62][63][64][65]. In particular a new ring-shaped potential has been introduced paving the way to new calculations in which this potential has been combined with the Coulomb potential [59], Hulthén potential [60] and Kratzer potential [61]. Later on, a more general form of this ring shaped potential has been applied with a q-deformed Woods-Saxon potential [62].…”

“…Very recently, we obtained general analytical solutions of Schrödinger equation in the context of position dependent effective mass for a class of non central physical potentials [66], involving in particular the Coulomb potential combined with several generalized versions forms of ring-shape such as double ring-shaped potential and novel angle-dependent (NAD) potential. The results of these calculations with non-central potentials may have interesting applications, particularly in quantum chemistry such as the study of ring-shaped molecules like cyclic polyenes and benzene [61].…”

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

“…The complete exact energy bound-state solution and the corresponding wave functions of a class of non-central potentials [65] have been solved recently by means of the Nikiforov-Uvarov (NU) method [65][66][67][68][69][70][71][72]. Very recently, Cheng and Dai [73], proposed a new potential consisting of a modified Kratzer's potential [75] plus the new proposed ring-shaped potential in [64]. They have presented the energy eigenvalues for this proposed exactly-solvable non-central potential in 3D-SE using the NU method.…”

“…[64,73] are closely relevant to each other as they deal with a Coulombic field interaction except for an additional centrifugal potential barrier acting as a repulsive core which for any arbitrary angular momentum prevents collapse of the system in any dimensional space due to this additional perturbation to the original angular momentum barrier. In very recent works [76][77][78], we have obtained analytically the exact energy eigenvalues and the corresponding normalized wave functions of the SE in D-dimensions with the proposed ring-shaped modified Kratzer potential [76] and the ring-shaped modified Coulomb potential [77,78] using the NU method [65][66][67][68][69][70][71][72][73][75][76][77][78]. The purpose of this work is to solve the SE for the pseudoharmonic plus ring-shaped potential offered in [64].…”

“…This new proposed potential falls amongst the class of noncentral potentials which have been solved in [64]. In spherical coordinates, we have given this appellation to the non-central potential [24,73] …”