Exact numeric calculation of nonparabolicity of exciton dispersion in semiconductors with degenerate valence band

An exact numerical calculation of the exciton dispersion in GaAs is performed, including all possible terms of the exciton Hamiltonian that arise from the electron and hole Hamiltonians. It is shown that the coupling of states of heavy-hole and light-hole excitons, described by the terms related to cubic anisotropy of the valence band, leads to nonparabolicity of the dispersion dependence of their energy on the wave vector. An analysis of reflection spectra of GaAs/AlGaAs heterostructures with wide quantum wells shows, however, that the states of quantisation of exciton motion observed in experiments can be described with good accuracy within a simple parabolic dispersion model. This contradiction between theory and experiment is discussed.