Nonlinear Supersymmetry for Spectral Design in Quantum Mechanics
  Nonlinear (Polynomial, N-fold) SUSY approach to preparation of quantum systems with pre-planned spectral properties is reviewed. The full classification of ladder-reducible and irreducible chains of SUSY algebras in one-dimensional QM is given. Possible extensions of SUSY in one dimension are described. They include (no more than) ${\cal N} =2$ extended SUSY with two nilpotent SUSY charges which generate the hidden symmetry acting as a central charge. Embedding stationary quantum systems into a non-stationary SUSY QM is shown to yield new insight on quantum orbits and on spectrum generating algebras. 
A. A. Andrianov (1 and 2) and F. Cannata (2) ((1) Sankt-Petersburg   State U.,(2) INFN, Bologna)