Symmetries and Supersymmetries of Generalized Schr\"odinger equations

zbMATH Open1488.35017arXiv2002.06438MaRDI QIDQ5153084

A. G. Nikitin

Publication date: 28 September 2021

Abstract: In this survey the contemporary results concerning supersymmetries in generalized Schr"odinger equations are presented. Namely, position dependent mass Sch"odinger equations are discussed as well as the equations with matrix potentials. An extended number of realistic quantum mechanical problems admitting extended supersymmetries is described, an extended class of matrix potentials is classified.

Full work available at URL: https://arxiv.org/abs/2002.06438

zbMATH Keywords

integrabilitysupersymmetryLie symmetryshape invariancesuperintegrabilityposition dependent massmatrix potential

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (3)

Supersymmetry of generalized linear Schrödinger equations in \((1+1)\) dimensions ⋮ General Schlesinger Systems and Their Symmetry from the View Point of Twistor theory ⋮ Master symmetries, non-Hamiltonian symmetries and superintegrability of the generalized Smorodinsky-Winternitz system

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