Exactly solvable two-dimensional Schrodinger operators and Laplace transformations

Details Exactly solvable two-dimensional Schrodinger operators and Laplace transformations Exactly solvable two-dimensional Schrodinger operators and Laplace transformations

2000-03-10

arxiv.org/abs/math-ph/0003008v1

Solitons, geometry, and topology: on the crossroad, 109--132, Amer. Math. Soc. Transl. Ser. 2, 179, Amer. Math. Soc., Providen

Physics

Mathematical Physics

AMSTeX, 25 pages

Scientific paper

Different cases of sequences of the Laplace Transformations for the 2D Schrodinger operator in the periodic magnetic field and electric potential are considered. They lead to the exactly solvable operators with nonstandard spectral properties including the double-periodic operators with algebraic Fermi surface known from the periodic soliton theory. Two appendices are added. In the Appendix I (the author - S. Novikov) two discretizations of the 2D operators and Laplace transformations are constructed. In the Appendix II (the authors - S. Novikov and I. Taimanov) some nonstandard 1D discrete operators are constructed with very interesting spectral properties.

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