2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/88875A 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.17 pages of REVTEXQuantum PhysicsNuclear Theorytext