We show that shape invariance appears when a quantum mechanical model is
invariant under a centrally extended superalgebra endowed with an additional
symmetry generator, which we dub the shift operator. The familiar mathematical
and physical results of shape invariance then arise from the BPS structure
associated with this shift operator. The shift operator also ensures that there
is a one-to-one correspondence between the energy levels of such a model and
the energies of the BPS-saturating states. These findings thus provide a more
comprehensive algebraic setting for understanding shape invariance.Comment: 15 pages, 2 figures, LaTe
