PERTURBATIVE APPROACH TO IMPURITY STATES IN ANISOTROPIC CRYSTALS

Two perturbative schemes have been developed to solve the anisotropic effective-mass Hamiltonian H = (p2x + p2y)/2mt + p2z/2m1 - e2/(Kr) for an impurity in a crystal. One is for the case mt/m1 ≪ 1. A combination of an adiabatic approach with the usual power series expansion shows that the actual expansion parameter is (mt/ml) 1 3 rather than the (mt/ml) 1 2 that one might expect on intuitive ground. The other case is for mt ≈ ml. Good accuracy can be achieved by including terms of higher order in the expansion parameter ∥1 - mt/ml∥. Numerical examples are given. © 1979.