  Binding energies of negative and positive trions in doped GaAs quantum wells
in high magnetic fields are studied by exact numerical diagonalization in
spherical geometry. Compared to earlier calculations, finite width of the
quantum well and its asymmetry caused by one-sided doping are both fully taken
into account by using self-consistent subband wave functions in the integration
of Coulomb matrix elements, and by inclusion of higher subbands along with
several Landau levels in the Hilbert space. Detailed analysis of the accuracy
and convergence of the exact diagonalization scheme is presented, including
dependence on Landau level and subband mixing, sensitivity to the (not well
known) single-particle spectrum in the valence band, and the estimate of
finite-size errors. The main results are the exciton dispersion and trion
binding energy spectrum calculated as a function of the magnetic field, quantum
well width, electron concentration, and the presence of an ionized impurity. As
a complementary approach, a combination of the exact diagonalization in the
quantum well plane and the variational calculation in the normal direction is
used as well.
