Solutions to the Schrödinger equation for two or more simple potentials are used to construct, in closed form, solutions for relatively complicated potentials.
An exact closed form of solution to the hyperradial Schrödinger equation is constructed for any general case comprising any hypercentral power and inverse-power potential. 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 ,…, r N ). This article is mainly devoted to the dernonstrat of the fact that any ψ of the form ψ = powerseries×exp(polynomial) = [ f ( x )exp ( g ( x ))] is potentially a solution of the Schrödinger equation, where the polynomial g( x ) is an ansatz depending on the interaction potential.