Binding energies and wave functions of wannier excitons in uniaxial crystals — a modified perturbation approach. I. theory

The effective mass Hamiltonian for excitons in uniaxial crystals is discussed by means of a modified perturbation approach. This approximation scheme gives upper limits for the exact energies; the validity of the approach is tested by deriving lower limits for the exact energies. The spacing of the two limits is shown to be satisfactorily small in a wide range of the anisotropy parameter. This parameter free approach leads to energies, which show good agreement with the results of involved variational calculations. In addition analytical expressions are obtained for the wave functions, which are easy to handle and can be used in more complex situations e.g. to include the description of external field influences.