Hyperspherical theory of anisotropic exciton
  A new approach to the theory of anisotropic exciton based on Fock transformation, i.e., on a stereographic projection of the momentum to the unit 4-dimensional (4D) sphere, is developed. Hyperspherical functions are used as a basis of the perturbation theory. The binding energies, wave functions and oscillator strengths of elongated as well as flattened excitons are obtained numerically. It is shown that with an increase of the anisotropy degree the oscillator strengths are markedly redistributed between optically active and formerly inactive states, making the latter optically active. An approximate analytical solution of the anisotropic exciton problem taking into account the angular momentum conserving terms is obtained. This solution gives the binding energies of moderately anisotropic exciton with a good accuracy and provides a useful qualitative description of the energy level evolution. 
E. A. Muljarov, A. L. Yablonskii, S. G. Tikhodeev, A. E. Bulatov, and   Joseph L. Birman
math-ph cond-mat.other math.MP quant-ph