A Class of Partially Solvable Two-Dimensional Quantum Models with Periodic Potentials
arXiv:0706.1344 · doi:10.1016/j.nuclphysb.2007.07.010
Abstract
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.
22 pages; some typos corrected; new reference added
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- Quasi-exactly solvable relativistic soft-core Coulomb models
- Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
- Supersymmetrical Separation of Variables for Scarf II Model: Partial Solvability
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- Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force
- Supersymmetric partners for the associated Lame potentials
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