  Exciton excited states in the quantum well are studied via their effect on
the nonradiative broadening of the ground exciton resonance. Dependence of the
nonradiative broadening of the ground exciton state on the photon energy of
additional laser excitation was measured. Applying magnetic field up to 6 T, we
could trace the formation of Landau levels and evolution of the exciton states
of size quantization in a 14-nm GaAs/AlGaAs quantum well. Sensitivity of the
technique allowed for observation of the second exciton state of size
quantization, unavailable for conventional reflectance and photoluminescence
spectroscopy. Our interpretation is supported by the numerical calculation of
the exciton energies of the heavy-hole and light-hole subsystems. The numerical
problems were solved using the finite-difference method on the nonuniform grid.
The ground Landau level of the free electron-hole pair was observed and
numerically analysed. In addition to energies of the excited states, electron
hole distances and exciton-light interaction constant was investigated using
the obtained in the numerical procedure exciton wave functions.
