  Algebraic approach to the integrability condition called shape invariance is
briefly reviewed. Various applications of shape-invariance available in the
literature are listed. A class of shape-invariant bound-state problems which
represent two-level systems are examined. These generalize the Jaynes-Cummings
Hamiltonian. Coherent states associated with shape-invariant systems are
discussed. For the case of quantum harmonic oscillator the decomposition of
identity for these coherent states is given. This decomposition of identity
utilizes Ramanujan's integral extension of the beta function.
