# Resolvent and Scattering Matrix at the Maximum of the Potential

Alexandrova, Ivana; Bony, Jean-François; Ramond, Thierry

Serdica Mathematical Journal (2008)

- Volume: 34, Issue: 1, page 267-310
- ISSN: 1310-6600

## Access Full Article

top## Abstract

top## How to cite

topAlexandrova, Ivana, Bony, Jean-François, and Ramond, Thierry. "Resolvent and Scattering Matrix at the Maximum of the Potential." Serdica Mathematical Journal 34.1 (2008): 267-310. <http://eudml.org/doc/281490>.

@article{Alexandrova2008,

abstract = {2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.We study the microlocal structure of the resolvent of the semiclassical Schrödinger operator with short range potential at an energy which is a unique non-degenerate global maximum of the potential. We prove that it is a semiclassical Fourier integral operator quantizing the incoming and outgoing Lagrangian submanifolds associated to the fixed hyperbolic point. We then discuss two applications of this result to describing the structure of the spectral function and the scattering matrix of the Schrödinger operator at the critical energy.},

author = {Alexandrova, Ivana, Bony, Jean-François, Ramond, Thierry},

journal = {Serdica Mathematical Journal},

keywords = {Scattering Matrix; Resolvent; Spectral Function; Schrödinger Equation; Fourier Integral Operator; Critical Energy; semi-classical Schrödinger operator; scattering matrix and amplitude},

language = {eng},

number = {1},

pages = {267-310},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Resolvent and Scattering Matrix at the Maximum of the Potential},

url = {http://eudml.org/doc/281490},

volume = {34},

year = {2008},

}

TY - JOUR

AU - Alexandrova, Ivana

AU - Bony, Jean-François

AU - Ramond, Thierry

TI - Resolvent and Scattering Matrix at the Maximum of the Potential

JO - Serdica Mathematical Journal

PY - 2008

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 34

IS - 1

SP - 267

EP - 310

AB - 2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.We study the microlocal structure of the resolvent of the semiclassical Schrödinger operator with short range potential at an energy which is a unique non-degenerate global maximum of the potential. We prove that it is a semiclassical Fourier integral operator quantizing the incoming and outgoing Lagrangian submanifolds associated to the fixed hyperbolic point. We then discuss two applications of this result to describing the structure of the spectral function and the scattering matrix of the Schrödinger operator at the critical energy.

LA - eng

KW - Scattering Matrix; Resolvent; Spectral Function; Schrödinger Equation; Fourier Integral Operator; Critical Energy; semi-classical Schrödinger operator; scattering matrix and amplitude

UR - http://eudml.org/doc/281490

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.