Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
A. A. Andrianov, M. V. Ioffe
TL;DR
This paper reviews the nonlinear supersymmetric approach to quantum systems, exploring its multidimensional extensions, algebraic classifications, and the emergence of hidden symmetries and spectrum-generating algebras in one- and two-dimensional quantum mechanics.
Contribution
It provides a comprehensive review of nonlinear SUSY in quantum mechanics, including classifications, multidimensional extensions, and the role of hidden symmetries.
Findings
Classification of SUSY algebra chains in 1D QM
Identification of hidden symmetries in nonlinear SUSY systems
Extension of nonlinear SUSY concepts to multidimensional quantum systems
Abstract
Nonlinear SUSY approach to preparation of quantum systems with pre-planned spectral properties is reviewed. Possible multidimensional extensions of Nonlinear SUSY are described. The full classification of ladder-reducible and irreducible chains of SUSY algebras in one-dimensional QM is given. Emergence of hidden symmetries and spectrum generating algebras is elucidated in the context of Nonlinear SUSY in one- and two-dimensional QM.
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