  A class of shape-invariant bound-state problems which represent transitions
in a two-level system introduced earlier are generalized to include arbitrary
energy splittings between the two levels. We show that the coupled-channel
Hamiltonians obtained correspond to the generalization of the non-resonant
Jaynes-Cummings Hamiltonian, 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.
