Geodesic
Schrödinger operator eigenvalue (resonance) on a zone boundary
Teoretičeskaâ i matematičeskaâ fizika, Tome 126 (2001) no. 2, pp. 196-205 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a Schrödinger operator with a periodic potential perturbed by a function periodic with respect to two variables and tending to zero with respect to the third variable, conditions are found under which a level (eigenvalue or resonance) falls on a zone boundary. The passage of the level through the boundary under variation of the perturbation magnitude is discussed. 
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     author = {Yu. P. Chuburin},
     title = {Schr\"odinger operator eigenvalue (resonance) on a zone boundary},
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Yu. P. Chuburin. Schrödinger operator eigenvalue (resonance) on a zone boundary. Teoretičeskaâ i matematičeskaâ fizika, Tome 126 (2001) no. 2, pp. 196-205. http://geodesic.mathdoc.fr/item/TMF_2001_126_2_a1/

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