Supersymmetric quantum mechanics is a convenient conventional name
for the description of systems whose Hamiltonian K  coincides with
one of the generators of the graded Lie algebra sl(1|1). One of
its main applications occurred in studies of solvable potentials
$V_{\pm}$ where the operator K is usually represented as a direct
sum of two ``ordinary" one-dimensional single-particle
Hamiltonians $H_{\pm} = p^2+V_{\pm}$ which are factorized, $H_{+}
=A^{+} A^{-}$, $H_{-} =A^{-} A^{+}$. In this framework, the
authors employ a re-factorization of $H_{+} =B^{+} B^{-}$ (where
$B^{+}= A^{+}T$ while $B^{-}= T^{-1}A^{-}$) and describe some of
its consequences, viz., a ``subtle" modification of the so called
(1) shape-invariance of the related solvable potentials (involving
now also a translation of parameters), (2) ``ladder" (i.e.,
creation and annihilation) operators. Explicit square-well- and
Hulth\'{e}n-potential illustrations are offered.




MR2100322 Filho, Elso Drigo ; Ricotta, Regina Maria . Ladder
operators for subtle hidden shape-invariant potentials. J. Phys. A
37 (2004), no. 43, 10057--10064.