ON SOLVING THE SCHRÖDINGER-LIKE WAVE EQUATION IN N DIMENSIONS FOR GENERALIZED SEXTIC AND OCTIC POTENTIALS

Abstract

For a potential of the type [Formula: see text], where n=6, 8, we obtain an exact analytic solution of the Schrödinger-like wave equation generalized to N dimensions. We make use of an ansatz for the eigenfunction and obtain a closed form expression for the energy eigenvalues at the cost of certain constraints on the potential parameters, bk. A distinct feature for even power potentials is pointed out for the case b0=0.