Perturbation Theory of Resonances and Embedded Eigenvalues of the Schrodinger Operator For a Crystal Film
Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 3, pp. 417-430
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We obtain formulas for resonances and eigenvalues embedded in the continuous spectrum that are similar to formulas in the standard perturbation theory. We prove that although the imaginary part of the first-order correction to the eigenvalue embedded in the continuous spectrum is zero, the perturbed eigenfunction, as a rule, ceases to be square-summable.
Keywords:
Schrodinger operator, perturbation theory, resonance, eigenvalue.
@article{TMF_2005_143_3_a6,
author = {Yu. P. Chuburin},
title = {Perturbation {Theory} of {Resonances} and {Embedded} {Eigenvalues} of the {Schrodinger} {Operator} {For} a {Crystal} {Film}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {417--430},
publisher = {mathdoc},
volume = {143},
number = {3},
year = {2005},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2005_143_3_a6/}
}
TY - JOUR AU - Yu. P. Chuburin TI - Perturbation Theory of Resonances and Embedded Eigenvalues of the Schrodinger Operator For a Crystal Film JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2005 SP - 417 EP - 430 VL - 143 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2005_143_3_a6/ LA - ru ID - TMF_2005_143_3_a6 ER -
%0 Journal Article %A Yu. P. Chuburin %T Perturbation Theory of Resonances and Embedded Eigenvalues of the Schrodinger Operator For a Crystal Film %J Teoretičeskaâ i matematičeskaâ fizika %D 2005 %P 417-430 %V 143 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2005_143_3_a6/ %G ru %F TMF_2005_143_3_a6
Yu. P. Chuburin. Perturbation Theory of Resonances and Embedded Eigenvalues of the Schrodinger Operator For a Crystal Film. Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 3, pp. 417-430. http://geodesic.mathdoc.fr/item/TMF_2005_143_3_a6/