19 research outputs found
A Class of Partially Solvable Two-Dimensional Quantum Models with Periodic Potentials
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.Comment: 22 pages; some typos corrected; new reference adde