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

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.


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