Calculation of the Eigenstates and Eigenvalues for the Power and Inverse-Power Hypercentral Potentials

Abstract

The bound-state solutions to the hyperradial Schrodinger equation is constructed for any general case comprising any hypercentral power and inverse-power potentials. The hypercentral potential depends only on the hyperradius which itself is a function of Jacobi relative coordinates that are functions of particle positions (r 1,r 2, … , and r N ). This paper is mainly devoted to the demonstration of the fact that any ψ of the form ψ = power series × exp(polynomial) = [f(x) exp (g(x))] is potentially a solution of the Schrodinger equation, where the polynomial g(x) is an ansatz depending on the interaction potential.