Self-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians

Language: English

Published by Springer International Publishing Apr 2023, 2023

3031108841 / 9783031108846

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Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, GermanyBuchWeltWeit Ludwig Meier e.K.

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This item is printed on demand - it takes 3-4 days longer - Neuware -This book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann and Krein-Vishik-Birman extension schemes both in their modern form and from a historical perspective, and provides a detailed analysis of a range of applications beyond the standard pedagogical examples (the latter are indexed in a final appendix for the reader's convenience).Self-adjointness of operators on Hilbert space representing quantum observables, in particular quantum Hamiltonians, is required to ensure real-valued energy levels, unitary evolution and, more generally, a self-consistent theory. Physical heuristics often produce candidate Hamiltonians that are only symmetric: their extension to suitably larger domains of self-adjointness, when possible, amounts to declaring additional physical states the operator must act on in order to have a consistent physics, and distinct self-adjoint extensions describe different physics.Realising observables self-adjointly is the first fundamental problem of quantum-mechanical modelling.The discussed applications concern models of topical relevance in modern mathematical physics currently receiving new or renewed interest, in particular from the point of view of classifying self-adjoint realisations of certain Hamiltonians and studying their spectral and scattering properties. The analysis also addresses intermediate technical questions such as characterising the corresponding operator closures and adjoints. Applications include hydrogenoid Hamiltonians, Dirac-Coulomb Hamiltonians, models of geometric quantum confinement and transmission on degenerate Riemannian manifolds of Grushin type, and models of few-body quantum particles with zero-range interaction.Graduate students and non-expert readers will benefit from a preliminary mathematical chapter collecting all the necessary pre-requisites on symmetric and self-adjoint operators on Hilbert space (including the spectral theorem), and from a further appendix presenting the emergence from physical principles of the requirement of self-adjointness for observables in quantum mechanics. 564 pp. Englisch.

Seller Inventory # 9783031108846

Title
Self-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians
Author
Matteo Gallone
Publisher
Springer International Publishing Apr 2023
Publication year
2023
Condition
Neu
Binding
Buch
Language
English
ISBN 10
3031108841
ISBN 13
9783031108846
Item weight
1,004 grams
Dimensions
241x160x36 mm

BuchWeltWeit Ludwig Meier e.K.

Bergisch Gladbach, Germany

5-star seller

AbeBooks seller since January 11, 2012

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BuchWeltWeit Ludwig Meier e.K.

Germany