  In this paper we investigate the shape invariance property of a potential in
one dimension. We show that a simple ansatz allows us to reconstruct all the
known shape invariant potentials in one dimension. This ansatz can be easily
extended to arrive at a large class of new shape invariant potentials in
arbitrary dimensions. A reformulation of the shape invariance property and
possible generalizations are proposed. These may lead to an important extension
of the shape invariance property to Hamiltonians that are related to standard
potential problems via space time transformations, which are found useful in
path integral formulation of quantum mechanics.
