Fundamentals of scattering theory and resonances in quantum mechanics

ABSTRACT We present the basics of two-body quantum-mechanical scattering theory and the theory of quantum resonances. The wave operators and S-matrix are constructed for smooth, compactly-supported potential perturbations of the Laplacian. The meromorphic continuation of the cut-off resolvent is pro...

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Autor principal:	Hislop,Peter D
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2012
Materias:	Scattering theory resonances Schrödinger equation wave operators quantum mechanics
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000300001
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spelling	oai:scielo:S0719-064620120003000012018-10-08Fundamentals of scattering theory and resonances in quantum mechanicsHislop,Peter D Scattering theory resonances Schrödinger equation wave operators quantum mechanics ABSTRACT We present the basics of two-body quantum-mechanical scattering theory and the theory of quantum resonances. The wave operators and S-matrix are constructed for smooth, compactly-supported potential perturbations of the Laplacian. The meromorphic continuation of the cut-off resolvent is proved for the same family of Schrödinger operators. Quantum resonances are defined as the poles of the meromorphic continuation of the cut-off resolvent. These are shown to be the same as the poles of the meromorphically continued S-matrix. The basic problems of the existence of resonances and estimates on the resonance counting function are described and recent results are presented.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.14 n.3 20122012-10-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000300001en10.4067/S0719-06462012000300001
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Scattering theory resonances Schrödinger equation wave operators quantum mechanics
spellingShingle	Scattering theory resonances Schrödinger equation wave operators quantum mechanics Hislop,Peter D Fundamentals of scattering theory and resonances in quantum mechanics
description	ABSTRACT We present the basics of two-body quantum-mechanical scattering theory and the theory of quantum resonances. The wave operators and S-matrix are constructed for smooth, compactly-supported potential perturbations of the Laplacian. The meromorphic continuation of the cut-off resolvent is proved for the same family of Schrödinger operators. Quantum resonances are defined as the poles of the meromorphic continuation of the cut-off resolvent. These are shown to be the same as the poles of the meromorphically continued S-matrix. The basic problems of the existence of resonances and estimates on the resonance counting function are described and recent results are presented.
author	Hislop,Peter D
author_facet	Hislop,Peter D
author_sort	Hislop,Peter D
title	Fundamentals of scattering theory and resonances in quantum mechanics
title_short	Fundamentals of scattering theory and resonances in quantum mechanics
title_full	Fundamentals of scattering theory and resonances in quantum mechanics
title_fullStr	Fundamentals of scattering theory and resonances in quantum mechanics
title_full_unstemmed	Fundamentals of scattering theory and resonances in quantum mechanics
title_sort	fundamentals of scattering theory and resonances in quantum mechanics
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2012
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000300001
work_keys_str_mv	AT hisloppeterd fundamentalsofscatteringtheoryandresonancesinquantummechanics
_version_	1714206778807287808

Fundamentals of scattering theory and resonances in quantum mechanics

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