Functional Analysis and Operator Theory for Quantum Physics

0477617 - ÚJF 2018 RIV CH eng M - Monography Chapter
Behrndt, J. - Langer, M. - Lotoreichik, Vladimir
Trace formulae for Schrödinger operators with singular interactions.
Functional Analysis and Operator Theory for Quantum Physics. Vol. 175. The Pavel Exner Anniversary Volume. Zürich: European Mathematical Society, 2017 - (Dittrich, J.; Kovařík, H.; Laptev, A.), s. 129-152. Series of Congress Reports. ISBN 978-3-03719-175-0
R&D Projects: GA ČR(CZ) GA14-06818S
Institutional support: RVO:61389005
Keywords : Schrödinger operators * point interactions * metric graphs * quantum waveguides * eigenvalue estimates * operator-valued functions * Cayley-Hamilton theorem * adiabatic theorem
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Dedicated with great pleasure to our teacher, colleague and friend Pavel Exner on the occasion of his 70th birtday.
This volume is dedicated to Pavel Exner on the occasion of his 70th anniversary. It collects contributions by numerous scientists with expertise in mathematical physics and in particular in problems arising from quantum mechanics. The questions addressed in the contributions cover a large range of topics. A lot of attention was paid to differential operators with zero range interactions, which are often used as models in quantum mechanics. Several authors considered problems related to systems with mixed-dimensions such as quantum waveguides, quantum layers and quantum graphs. Eigenvalues and eigenfunctions of Laplace and Schrödinger operators are discussed too, as well as systems with adiabatic time evolution. Although most of the problems treated in the book have a quantum mechanical background, some contributions deal with issues which go well beyond this framework, for example the Cayley–Hamilton theorem, approximation formulae for contraction semigroups or factorization of analytic operator-valued Fredholm functions. As for the mathematical tools involved, the book provides a wide variety of techniques from functional analysis and operator theory.
Altogether the volume presents a collection of research papers which will be of interest to any active scientist working in one of the above mentioned fields.
Permanent Link: http://hdl.handle.net/11104/0273912