%0 Journal Article %1 1751-8121-45-50-503001 %A Andrianov, A A %A Ioffe, M V %D 2012 %J Journal of Physics A: Mathematical and Theoretical %K mechanics physics quantum review susy unread %N 50 %P 503001 %T Nonlinear supersymmetric quantum mechanics: concepts and realizations %U http://stacks.iop.org/1751-8121/45/i=50/a=503001 %V 45 %X The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum mechanics (QM) is reviewed. Its building from the chains (ladders) of linear SUSY systems is outlined and different one-dimensional and two-dimensional realizations are described. It is elaborated how the nonlinear SUSY approach provides two new methods of SUSY separation of variables for various two-dimensional models. In the framework of these methods, a partial and/or complete solution of some two-dimensional models becomes possible. The full classification of ladder-reducible and irreducible chains of SUSY algebras in one-dimensional QM is given. The emergence of hidden symmetries and spectrum generating algebras is elucidated in the context of the nonlinear SUSY in one-dimensional stationary and non-stationary, as well as in two-dimensional QM.

@article{1751-8121-45-50-503001, abstract = {The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum mechanics (QM) is reviewed. Its building from the chains (ladders) of linear SUSY systems is outlined and different one-dimensional and two-dimensional realizations are described. It is elaborated how the nonlinear SUSY approach provides two new methods of SUSY separation of variables for various two-dimensional models. In the framework of these methods, a partial and/or complete solution of some two-dimensional models becomes possible. The full classification of ladder-reducible and irreducible chains of SUSY algebras in one-dimensional QM is given. The emergence of hidden symmetries and spectrum generating algebras is elucidated in the context of the nonlinear SUSY in one-dimensional stationary and non-stationary, as well as in two-dimensional QM.}, added-at = {2013-02-17T02:15:23.000+0100}, author = {Andrianov, A A and Ioffe, M V}, biburl = {https://www.bibsonomy.org/bibtex/267af9912d24948652da37df18f2364f3/drmatusek}, interhash = {c0a2e7373b51b84ea3dc3b3caf89cae0}, intrahash = {67af9912d24948652da37df18f2364f3}, journal = {Journal of Physics A: Mathematical and Theoretical}, keywords = {mechanics physics quantum review susy unread}, month = dec, number = 50, pages = 503001, timestamp = {2013-02-17T02:15:46.000+0100}, title = {Nonlinear supersymmetric quantum mechanics: concepts and realizations}, url = {http://stacks.iop.org/1751-8121/45/i=50/a=503001}, volume = 45, year = 2012 }