Exact solution of the Schrödinger equation for the modified Kratzer potential plus a ring-shaped potential by the Nikiforov–Uvarov method. (English) Zbl 1111.81043

Cheng, Yan-Fu; Dai, Tong-Qing

Phys. Scr. 75, No. 3, 274-277 (2007).

Summary: We propose a new exactly solvable potential which consists of the modified Kratzer potential plus a new ring-shaped potential \(\beta\text{ ctg}^{2}\theta /r^{2}\). 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.

MSC:

81Q05	Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81U15	Exactly and quasi-solvable systems arising in quantum theory