EFFECTIVE-MASS APPROXIMATION FOR EXCITONS IN ANISOTROPIC CRYSTALS

In the effective-mass approximation, the Hamiltonian for an exciton in an anisotropic crystal may be separated into two parts, one of which is spherically symmetric. The second part contains the anisotropy of the reduced effective mass and of the dielectric constant. By means of perturbation theory and group-theoretical considerations, we have obtained correction terms for the zeroth-order energy eigenvalues which are continuous functions of the anisotropy parameter A=(μ ⊥/μ ∥)·(ε ⊥/ε ∥), where μ ⊥, μ ∥ and ε ⊥, ε ∥ are the components, perpendicular and parallel to the c-axis of the reduced mass and the dielectric constant. The correction terms depend on the orbital and magnetic quantum numbers l and m. The treatment shows how the degeneracies of the spherical problem are lifted and how the spherical eigenfunctions are mixed by the anisotropic potential. © 1969 Società Italiana di Fisica.