Nonlinear Supersymmetry for Spectral Design in Quantum Mechanics

Details Nonlinear Supersymmetry for Spectral Design in Quantum Mechanics Nonlinear Supersymmetry for Spectral Design in Quantum Mechanics

2004-07-10

arxiv.org/abs/hep-th/0407077v2

J.Phys. A37 (2004) 10297-10323

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, IOP style, talk at PSQM-2003 (Valladolid); minor corrections in refs

Scientific paper

10.1088/0305-4470/37/43/019

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.

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