Geodesic
The Lippmann--Schwinger equation for quantum wires
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2011), pp. 99-104

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We consider the discrete Schrodinger operator with a potential of a special form defined on a graph whose nodes lie on the union of two intersected straight lines. We prove that there exist unique quasi-levels (eigenvalues or resonances) in the neighborhoods of the point $\pm2$ (these points consist a boundary of the essential spectrum). The asymptotic formulae for quasi-levels are obtained. We find the conditions for the coefficient of reflection is equal to zero.
Keywords: eigenvalue, resonance, discrete Lippmann–Schwinger equation. 
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     author = {T. S. Tinyukova},
     title = {The {Lippmann--Schwinger} equation for quantum wires},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {99--104},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
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}
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T. S. Tinyukova. The Lippmann--Schwinger equation for quantum wires. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2011), pp. 99-104. http://geodesic.mathdoc.fr/item/VUU_2011_1_a9/