The exactly solvable eigenproblems in Schr\"odinger quantum mechanics
typically involve the differential "shift operators". In the standard
supersymmetric (SUSY) case, the shift operator turns out to be of first order.
In this work, I discuss a technique to generate exactly solvable eigenproblems
by using second order shift operators. The links between this method and SUSY
are analysed. As an example, we show the existence of a two-parametric family
of exactly solvable Hamiltonians, which contains the Abraham-Moses potentials
as a particular case.Comment: 7 pages, 2 encapsulated postscript figures, uses epsf.sty talk given
at the II International Workshop on Classical and Quantum Integrable Systems,
Dubna (Russia), 8-12 July (1996) to be published in Int. J. Mod. Phys.