Dual Jet Geometrization for Time-Dependent Hamiltonians and Applications, Neagu
Автор: Baaquie Название: Path Integrals and Hamiltonians ISBN: 1107009790 ISBN-13(EAN): 9781107009790 Издательство: Cambridge Academ Рейтинг: Цена: 21384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A succinct introduction to the powerful and flexible combination of Hamiltonian operators and path integrals in quantum mathematics, with a practical emphasis on methodological and mathematical aspects. Essential reading for researchers and graduate students in physics, and engineers whose work touches on quantum mechanics.
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.
Описание: This book presents the Proceedings of the 15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics, held in Palermo, Italy, from 18 to 23 May 2015.
Автор: Fabio Bagarello; Roberto Passante; Camillo Trapani Название: Non-Hermitian Hamiltonians in Quantum Physics ISBN: 3319313541 ISBN-13(EAN): 9783319313542 Издательство: Springer Рейтинг: Цена: 22203.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents the Proceedings of the 15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics, held in Palermo, Italy, from 18 to 23 May 2015.
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