  A variational calculation of the spin-singlet and spin-triplet state of a
negatively charged exciton (trion) confined to a single quantum well and in the
presence of a perpendicular magnetic field is presented. We calculated the
probability density and the pair correlation function of the singlet and
triplet trion states. The dependence of the energy levels and of the binding
energy on the well width and on the magnetic field strength was investigated.
We compared our results with the available experimental data on GaAs/AlGaAs
quantum wells and find that in the low magnetic field region (B<18 T) the
observed transition are those of the singlet and the dark triplet trion (with
angular momentum $L_z=-1$), while for high magnetic fields (B>25 T) the dark
trion becomes optically inactive and possibly a transition to a bright triplet
trion (angular momentum $L_z=0$) state is observed.
