Geodesic
Quasi-levels of the discrete Schr\"odinger operator for a~quantum waveguide
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2011), pp. 88-97

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We proved that the discrete Schrödinger operator corresponding to a quantum waveguide with a small exponentially decreasing potential has quasi-levels (eigenvalues or resonances). The asymptotic formulas for these quasi-levels are obtained.
Keywords: discrete Schrödinger equation, eigenvalue, resonance. 
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     author = {T. S. Tinyukova},
     title = {Quasi-levels of the discrete {Schr\"odinger} operator for a~quantum waveguide},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {88--97},
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     number = {2},
     year = {2011},
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T. S. Tinyukova. Quasi-levels of the discrete Schr\"odinger operator for a~quantum waveguide. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2011), pp. 88-97. http://geodesic.mathdoc.fr/item/VUU_2011_2_a5/