  We derive an exact solution of an explicitly time-dependent multichannel
model of quantum mechanical nonadiabatic transitions. Our model corresponds to
the case of a single linear diabatic energy level interacting with a band of an
arbitrary N states, for which the diabatic energies decay with time according
to the Coulomb law. We show that the time-dependent Schroedingier equation for
this system can be solved in terms of Meijer functions whose asymptotics at a
large time can be compactly written in terms of elementary functions that
depend on the roots of an Nth order characteristic polynomial. Our model can be
considered a generalization of the Demkov-Osherov model. In comparison to the
latter, our model allows one to explore the role of curvature of the band
levels and diabatic avoided crossings.
