  A negatively charged quasi-two dimensional exciton ($X^-$) is solved exactly
numerically in the presence of a uniform perpendicular B-field. Various
quasi-two dimensional geometries are studied. The charge distribution of the
$X^-$ parallel to the B-field is found to be crucial in determining the
stability of the optically-active $X^-$ and hence its photoluminescence (PL)
signature. The theory provides a quantitative explanation of recent
experimental results obtained for a GaAs quantum well. Effects are found which
cannot be described within a lowest Landau level approximation.
  PACS: 78.20.Ls 78.66.-w 73.20.Dx
