  Using a representation of multichannel quantum defect theory in terms of a
quantum Poincar\'e map for bound Rydberg molecules, we apply Jung's scattering
map to derive a generalized quantum map, that includes the continuum. We show,
that this representation not only simplifies the understanding of the method,
but moreover produces considerable numerical advantages. Finally we show under
what circumstances the usual semi-classical approximations yield satisfactory
results. In particular we see that singularities that cause problems in
semi-classics are irrelevant to the quantum map.
