Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 064, 26 pages      arXiv:0906.0549      https://doi.org/10.3842/SIGMA.2009.064
Contribution to the Proceedings of the VIIth Workshop ''Quantum Physics with Non-Hermitian Operators''

Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics

Alexander A. Andrianov a, b and Andrey V. Sokolov a
a) V.A.Fock Department of Theoretical Physics, Sankt-Petersburg State University, 198504 St. Petersburg, Russia
b) Departament ECM and ICCUB, Departament de Fisica, Universitat de Barcelona, 08028 Barcelona, Spain

Received March 05, 2009, in final form June 02, 2009; Published online June 17, 2009

Abstract
When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples.

Key words: supersymmetric quantum mechanics; periodic potentials; hidden symmetry.

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