  A class of shape-invariant bound-state problems which represent transition in
a two-level system introduced earlier are generalized to include arbitrary
energy splittings between the two levels as well as intensity-dependent
interactions. We show that the couple-channel Hamiltonians obtained correspond
to the generalizations of the nonresonant and intensity-dependent nonresonant
Jaynes-Cummings Hamiltonians, widely used in quantized theories of laser. In
this general context, we determine the eigenstates, eigenvalues, the time
evolution matrix and the population inversion matrix factor.
