Gallone Self-adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians 9783031108846

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Автор: Gallone
Название: Self-adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians
ISBN: 9783031108846
Издательство: Springer
Классификация:

Основы высшей математики и математический анализ

Математическая физика

ISBN-10: 3031108841
Обложка/Формат: Hardback
Страницы: 538
Вес: 1.00 кг.
Дата издания: 05.04.2023
Серия: Springer Monographs in Mathematics
Язык: English
Издание: 1st ed. 2023
Иллюстрации: 13 tables, color; 13 illustrations, color; xxv, 538 p. 13 illus. in color.
Размер: 235 x 155
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: 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.
Дополнительное описание: - Part I Theory. - 1. Generalities on Symmetric and Self-Adjoint Operators on Hilbert Space. - 2. Classical Self-Adjoint Extension Schemes. - Part II Applications. - 3. Hydrogenoid Spectra with Central Perturbations. - 4. Dirac-Coulomb Hamiltonians for He

Self-adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians, Gallone