A Class of Partially Solvable Two-Dimensional Quantum Models with Periodic Potentials

Details A Class of Partially Solvable Two-Dimensional Quantum Models with Periodic Potentials A Class of Partially Solvable Two-Dimensional Quantum Models with Periodic Potentials

2007-06-10

arxiv.org/abs/0706.1344v2

Nucl.Phys.B790:414-431,2008

Physics

High Energy Physics

High Energy Physics - Theory

22 pages; some typos corrected; new reference added

Scientific paper

10.1016/j.nuclphysb.2007.07.010

The supersymmetrical approach is used to analyse a class of two-dimensional quantum systems with periodic potentials. In particular, the method of SUSY-separation of variables allowed us to find a part of the energy spectra and the corresponding wave functions (partial solvability) for several models. These models are not amenable to conventional separation of variables, and they can be considered as two-dimensional generalizations of Lame, associated Lame, and trigonometric Razavy potentials. All these models have the symmetry operators of fourth order in momenta, and one of them (the Lame potential) obeys the property of self-isospectrality.

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