Geodesic
Estimate of the solution of the scattering problem for a one-dimensional trapping potential
Sbornik. Mathematics, Tome 188 (1997) no. 12, pp. 1731-1738 
A. A. Arsen'ev. Estimate of the solution of the scattering problem for a one-dimensional trapping potential. Sbornik. Mathematics, Tome 188 (1997) no. 12, pp. 1731-1738. http://geodesic.mathdoc.fr/item/SM_1997_188_12_a0/
@article{SM_1997_188_12_a0,
     author = {A. A. Arsen'ev},
     title = {Estimate of the solution of the~scattering problem for a~one-dimensional trapping potential},
     journal = {Sbornik. Mathematics},
     pages = {1731--1738},
     year = {1997},
     volume = {188},
     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_12_a0/}
}
TY  - JOUR
AU  - A. A. Arsen'ev
TI  - Estimate of the solution of the scattering problem for a one-dimensional trapping potential
JO  - Sbornik. Mathematics
PY  - 1997
SP  - 1731
EP  - 1738
VL  - 188
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/SM_1997_188_12_a0/
LA  - en
ID  - SM_1997_188_12_a0
ER  - 
%0 Journal Article
%A A. A. Arsen'ev
%T Estimate of the solution of the scattering problem for a one-dimensional trapping potential
%J Sbornik. Mathematics
%D 1997
%P 1731-1738
%V 188
%N 12
%U http://geodesic.mathdoc.fr/item/SM_1997_188_12_a0/
%G en
%F SM_1997_188_12_a0

Voir la notice de l'article provenant de la source Math-Net.Ru

A new method is proposed for estimating the imaginary part of the pole of the scattering matrix for a one-dimensional trapping potential. The method is based on the principle of wave operator invariance and on the Parseval equality for the continuous spectrum eigenfunctions.

[1] “Spesial Issue on Mesoscopic Physics”, J. Math. Phys., 37:10 (1996)

[2] Arsenev A. A., “Rezonansnye svoistva matritsy rasseyaniya dlya odnomernogo operatora Shredingera s lovushechnym potentsialom”, Matem. sb., 187:6 (1996), 3–20 | MR | Zbl

[3] Birman M. Sh., Entina S. B., “Statsionarnyi podkhod v abstraktnoi teorii rasseyaniya”, Izv. AN SSSR. Ser. matem., 31 (1967), 401–430 | MR | Zbl