Alexander A. Andrianov, Andrey V. Sokolov, “Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics”, SIGMA, 2009, Volume 5,064, 26 pp.

This article is cited in 12 papers

Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics

Alexander A. Andrianov^ab, 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

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.

Keywords: supersymmetric quantum mechanics; periodic potentials; hidden symmetry.

MSC: 81Q60; 81R15; 47B15

Received: March 5, 2009; in final form June 2, 2009; Published online June 17, 2009

Language: English

DOI: 10.3842/SIGMA.2009.064