BOUND-STATES FOR ANISOTROPIC POTENTIALS AND MASSES

A general method for finding the energies and wave functions for aniso tropic masses and potentials has been studied. This method uses basis wave functions expanded in spherical harmonics. The coupled differenti al equations for the radial components of each basis function are inte grated numerically. The energy eigenfunctions and their radial derivat ives are then matched at a spherical boundary. Special treatment is ne eded to ensure linear independence of the basis functions at the bound ary. The applicability of this method and the speed of convergence are tested on anisotropic harmonic oscillators. The method is then applie d to the Coulomb potential with anisotropic masses. With a basis of fi ve or fewer spherical harmonics, our method produces energies which co nverge to values lower than those previously reported. We have also ob tained energy levels for the Coulomb potential with threefold mass ani sotropy. This method should be applicable to other anisotropic problem s with a single potential minimum. In particular, it should facilitate the employment of full-potential Green-function band theory.