  For nonrelativistic Hamiltonians which are shape invariant, analytic
expressions for the eigenvalues and eigenvectors can be derived using the well
known method of supersymmetric quantum mechanics. Most of these Hamiltonians
also possess spectrum generating algebras and are hence solvable by an
independent group theoretic method. In this paper, we demonstrate the
equivalence of the two methods of solution by developing an algebraic framework
for shape invariant Hamiltonians with a general change of parameters, which
involves nonlinear extensions of Lie algebras.
