On small perturbations of the Schrodinger operator with a periodic potential

被引:15
作者
Chuburin, YP
机构
[1] Udmurtian Scientific Center of the Ural Branch of the Russian Academy of Sciences,Physicotechnical Institute
关键词
D O I
10.1007/BF02630460
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Consideration is given to small perturbations of a potential, periodic with respect to the variables x(j), j = 1, 2, 3, by a function periodic in x(1) and x(2) that decays exponentially as \x(3)\ --> infinity. It is shown that in the neighborhood of energies corresponding to the extrema in the third quasimomentum component of nondegenerate eigenvalues of the Schrodinger operator, with the periodic potential considered in a cell, there exists a unique solution (up to within a numerical factor) to the integral equation describing both the eigenvalues and resonance levels. The asymptotic behavior of the eigenvalues and resonance levels is investigated.
引用
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页码:351 / 359
页数:9
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