Nonlinear supersymmetry for spectral design in quantum mechanics

Abstract

Nonlinear (Polynomial, N-fold) SUSY approach to preparation of quantum\nsystems with pre-planned spectral properties is reviewed. The full\nclassification of ladder-reducible and irreducible chains of SUSY algebras in\none-dimensional QM is given. Possible extensions of SUSY in one dimension are\ndescribed. They include (no more than) ${\\cal N} =2$ extended SUSY with two\nnilpotent SUSY charges which generate the hidden symmetry acting as a central\ncharge. Embedding stationary quantum systems into a non-stationary SUSY QM is\nshown to yield new insight on quantum orbits and on spectrum generating\nalgebras.\n