Approximate shape-invariant potentials in quantum mechanics

We introduce and explore the concept of approximate shape invariance of par ametrized potential functions for non-relativistic one-dimensional quantum systems. The supersymmetric partner V-2 of an approximate shape-invariant p otential V-1 does not exhibit the same shape as the original potential. How ever, by an appropriate choice of the values of the relevant parameters, V- 2 can still be approximated by V-1. We also propose a measure for the degre e of shape invariance exhibited by a parametrized potential function. In or der to illustrate these ideas we consider (a) the Lillo-Mantegna potentials admitting exact analytic power-law ground-state wavefunctions, and (b) a f amily of potentials whose ground-state eigenfunctions are given by the tria l wavefunctions employed by Cooper, Dawson and Shepard in the SUSY-based va riational method.