Abstract

An exact closed form of solution to the hyperradialSchrödinger equation is constructed for any general casecomprising any hypercentral power and inverse-power potential.The hypercentral potential depends only on thehyperradius, which itself is a function of Jacobi relativecoordinates that are functions of particle positions(r1,r2,…, rN). Thisarticle is mainly devoted to the dernonstrat of the fact that anyψ of the form ψ = powerseries×exp(polynomial) = [f(x)exp (g(x))]is potentially a solution of the Schrödingerequation, where the polynomial g(x) is an ansatz depending on theinteraction potential.

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