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Dittrich J., Kovařík H., Laptev A. (Eds.) Functional Analysis and Operator Theory for Quantum Physics

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Dittrich J., Kovařík H., Laptev A. (Eds.) Functional Analysis and Operator Theory for Quantum Physics
European Mathematical Society, Zürich, Switzerlandm, 2017. — 597 p. — (EMS Series of Congress Reports). — ISBN:3037191759.
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 Schr?dinger 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.
Contents
Relative partition function of Coulomb plus delta interaction
Inequivalence of quantum Dirac elds of different masses and the underlying general structures involved
On a class of Schrödinger operators exhibiting spectral transition
On the quantum mechanical three-body problem with zero-range interactions
On the index of meromorphic operator-valued functions and some applications
Trace formulae for Schrödinger operators with singular interactions
An improved bound for the non-existence of radial solutions of the Brezis–Nirenberg problem in Hn
Twisted waveguide with a Neumann window
Example of a periodic Neumann waveguide with a gap in its
Two-dimensional time-dependent point interactions
On resonant spectral gaps in quantum graphs
Adiabatic theorem for a class of stochastic differential equations on a Hilbert space
Eigenvalues of Schrödinger operators with complex surface potentials
A lower bound to the spectral threshold in curved quantum layers
To the spectral theory of vector-valued Sturm–Liouville operators with summable potentials and point interactions
Spectral asymptotics for the Dirichlet Laplacian with a Neumann window via a Birman–Schwinger analysis of the Dirichlet-to-Neumann operator
Dirichlet eigenfunctions in the cube, sharpening the Courant nodal inequality
A mathematical modeling of electron–phonon interaction for small wave numbers close to zero
The modied unitary Trotter–Kato and Zeno product formulas revisited
Spectral asymptotics induced by approaching and diverging planar circles
Spectral estimates for the Heisenberg Laplacian on cylinders
Variational proof of the existence of eigenvalues for star graphs
On the boundedness and compactness of weighted Green operators of second-order elliptic operators
Abstract graph-like spaces and vector-valued metric graphs
A Cayley–Hamiltonian theorem for periodic nite band matrices
Path topology dependence of adiabatic time evolution
On quantum graph lters with at passbands
Comments on the Chernoff n-lemm
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