  Density of states (DOS) and absorption spectrum of weakly doped, narrow
quantum wells in high magnetic fields are calculated by realistic exact
diagonalization. The systems containing an electron--hole pair with and without
an additional, second electron are compared. In DOS, the exciton--electron
interaction is shown to fill the gaps between Landau levels and to yield
additional discrete peaks corresponding to bound trion states. In absorption,
interaction with the additional free electron causes no shift or
renormalization of main, excitonic peaks. However, it results in additional,
weaker peaks associated with bound trions in the lowest or higher Landau
levels. The calculation is supplemented with experimental photoluminescence and
photoluminescence-excitation studies of two-dimensional holes and electrons in
high magnetic fields.
