Solvable Noncentral Potentials

Using the ideas of supersymmetry and shape invariance we show that the eigenvalues and eigenfunctions of a wide class of noncentral potentials can be obtained in a closed form by the operator method. This generalization considerably extends the list of exactly solvable potentials for which the solution can be obtained algebraically in a simple and elegant manner. As an illustration, we discuss in detail the example of the potential V (r, θ, φ) = ω 4 r + δ r2 + C r2sin2θ + D r2cos2θ + F r2sin2θ sin2αφ + G r2sin2θ cos2αφ with 7 parameters.Other algebraically solvable examples are also given.