Geodesic
The resonance spectrum of a Schr\"odinger operator with a rapidly decaying potential
Sbornik. Mathematics, Tome 200 (2009) no. 12, pp. 1847-1880

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

Resonances of the one-dimensional Schrödinger operator are investigated, that is, the poles of the analytic extension of the corresponding scattering matrix. For a certain class of superexponentially decreasing potentials, including the Gaussian potential, the Born approximation is substantiated for the problem of localizing the poles of the scattering matrix. This makes it possible to find an asymptotic law (a quantization rule) for the distribution of these poles. For the first time, using the method developed in the paper, asymptotic formulae for resonances are obtained in the case of potentials with noncompact support. Bibliography: 15 titles.
Keywords: resonance, pole of a scattering matrix, asymptotic distribution, Schrödinger operator, superexponentially decreasing potential. 
@article{SM_2009_200_12_a5,
     author = {S. A. Stepin and A. G. Tarasov},
     title = {The resonance spectrum of a {Schr\"odinger} operator with a rapidly decaying potential},
     journal = {Sbornik. Mathematics},
     pages = {1847--1880},
     publisher = {mathdoc},
     volume = {200},
     number = {12},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2009_200_12_a5/}
}
TY  - JOUR
AU  - S. A. Stepin
AU  - A. G. Tarasov
TI  - The resonance spectrum of a Schr\"odinger operator with a rapidly decaying potential
JO  - Sbornik. Mathematics
PY  - 2009
SP  - 1847
EP  - 1880
VL  - 200
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2009_200_12_a5/
LA  - en
ID  - SM_2009_200_12_a5
ER  - 
%0 Journal Article
%A S. A. Stepin
%A A. G. Tarasov
%T The resonance spectrum of a Schr\"odinger operator with a rapidly decaying potential
%J Sbornik. Mathematics
%D 2009
%P 1847-1880
%V 200
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2009_200_12_a5/
%G en
%F SM_2009_200_12_a5
S. A. Stepin; A. G. Tarasov. The resonance spectrum of a Schr\"odinger operator with a rapidly decaying potential. Sbornik. Mathematics, Tome 200 (2009) no. 12, pp. 1847-1880. http://geodesic.mathdoc.fr/item/SM_2009_200_12_a5/