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Finite-zone, two-dimensional, potential Schrödinger operators. Explicit formulas and evolution equations. (English. Russian original) Zbl 0613.35020
Sov. Math., Dokl. 30, 588-591 (1984); translation from Dokl. Akad. Nauk SSSR 279, 20-24 (1984).
Explicit formulas for the eigenfunctions of two-dimensional, potential Schrödinger operators are given. The paper ends with the following conjecture: any smooth, real, doubly periodic potential V(x,y) can be approximated by potentials which are ”finite-zone with respect to one energy level”.
Reviewer: G.Moroşanu

MSC:
35J10 Schrödinger operator, Schrödinger equation
35P05 General topics in linear spectral theory for PDEs
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