Non-relativistic treatment of diatomic molecules interacting with a generalized Kratzer potential in hyperspherical coordinates. (English) Zbl 1213.81228

Durmus, Aysen

J. Phys. A, Math. Theor. 44, No. 15, Article ID 155205, 14 p. (2011).

Summary: We investigate solutions of a non-relativistic wave equation in hyperspherical coordinates for a diatomic molecule system interacting with a generalized Kratzer potential. Rovibrational eigenvalues and corresponding wavefunctions of non-relativistic diatomic molecules have been determined within the framework of the asymptotic iteration method. Certain fundamental conditions for the applications of the asymptotic iteration method, such as a suitable asymptotic form for the wave-function and the termination condition for the iteration process, are discussed. \(N\)-dimensional bound state eigenfunction solutions used in studying the dynamical variables of diatomic molecules are obtained in terms of a confluent hypergeometric function and a generalized Laguerre polynomial. This systematic approach is tested by calculating the rovibrational energy spectra of hydrogen and sodium chloride molecules.

MSC:

81V55	Molecular physics
33C55	Spherical harmonics
81Q05	Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics