Mathematical Challenges Of Zero Range Physics
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Mathematical Challenges Of Zero Range Physics
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Author : Alessandro Michelangeli
language : en
Publisher: Springer Nature
Release Date : 2021-02-04
Mathematical Challenges Of Zero Range Physics written by Alessandro Michelangeli and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-04 with Science categories.
Since long over the decades there has been a large transversal community of mathematicians grappling with the sophisticated challenges of the rigorous modelling and the spectral and scattering analysis of quantum systems of particles subject to an interaction so much localised to be considered with zero range. Such a community is experiencing fruitful and inspiring exchanges with experimental and theoretical physicists. This volume reflects such spirit, with a diverse range of original contributions by experts, presenting an up-to-date collection of most relevant results and challenging open problems. It has been conceived with the deliberate two-fold purpose of serving as an updated reference for recent results, mathematical tools, and the vast related literature on the one hand, and as a bridge towards several key open problems that will surely form the forthcoming research agenda in this field.
Analysis As A Tool In Mathematical Physics
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Author : Pavel Kurasov
language : en
Publisher: Springer Nature
Release Date : 2020-07-14
Analysis As A Tool In Mathematical Physics written by Pavel Kurasov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-14 with Mathematics categories.
Boris Pavlov (1936-2016), to whom this volume is dedicated, was a prominent specialist in analysis, operator theory, and mathematical physics. As one of the most influential members of the St. Petersburg Mathematical School, he was one of the founders of the Leningrad School of Non-self-adjoint Operators. This volume collects research papers originating from two conferences that were organized in memory of Boris Pavlov: “Spectral Theory and Applications”, held in Stockholm, Sweden, in March 2016, and “Operator Theory, Analysis and Mathematical Physics – OTAMP2016” held at the Euler Institute in St. Petersburg, Russia, in August 2016. The volume also includes water-color paintings by Boris Pavlov, some personal photographs, as well as tributes from friends and colleagues.
Proceedings Of The Xi International Conference Stochastic And Analytic Methods In Mathematical Physics
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Author : Boldrighini, Carlo
language : en
Publisher: Universitätsverlag Potsdam
Release Date : 2020
Proceedings Of The Xi International Conference Stochastic And Analytic Methods In Mathematical Physics written by Boldrighini, Carlo and has been published by Universitätsverlag Potsdam this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
The XI international conference Stochastic and Analytic Methods in Mathematical Physics was held in Yerevan 2 – 7 September 2019 and was dedicated to the memory of the great mathematician Robert Adol’fovich Minlos, who passed away in January 2018. The present volume collects a large majority of the contributions presented at the conference on the following domains of contemporary interest: classical and quantum statistical physics, mathematical methods in quantum mechanics, stochastic analysis, applications of point processes in statistical mechanics. The authors are specialists from Armenia, Czech Republic, Denmark, France, Germany, Italy, Japan, Lithuania, Russia, UK and Uzbekistan. A particular aim of this volume is to offer young scientists basic material in order to inspire their future research in the wide fields presented here.
Self Adjoint Extension Schemes And Modern Applications To Quantum Hamiltonians
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Author : Matteo Gallone
language : en
Publisher: Springer Nature
Release Date : 2023-04-04
Self Adjoint Extension Schemes And Modern Applications To Quantum Hamiltonians written by Matteo Gallone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-04 with Science categories.
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.
Problems Solutions In Theoretical Mathematical Physics Introductory Level
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Author : W.-H. Steeb
language : en
Publisher: World Scientific
Release Date : 2003
Problems Solutions In Theoretical Mathematical Physics Introductory Level written by W.-H. Steeb and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Science categories.
This book is a collection of problems with detailed solutions which will prove valuable to students and research workers in mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn important principles and strategies required for problem solving. Teachers will find this text useful as a supplement, since important concepts and techniques are developed through the problems. The material has been tested in the author's lectures given around the world. The book is divided into two volumes. Volume I presents the introductory problems, for undergraduate and advanced undergraduate students. In Volume II, the more advanced problems, together with detailed solutions, are collected, to meet the needs of graduate students and researchers. The problems included cover most of the new fields in theoretical and mathematical physics, such as Lax representation, Backlund transformation, soliton equations, Lie-algebra-valued differential forms, the Hirota technique, the Painleve test, the Bethe ansatz, the Yang -- Baxter relation, chaos, fractals, complexity, etc.
From Complex Analysis To Operator Theory A Panorama
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Author : Malcolm Brown
language : en
Publisher: Springer Nature
Release Date : 2023-09-21
From Complex Analysis To Operator Theory A Panorama written by Malcolm Brown and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-21 with Mathematics categories.
This volume is dedicated to the memory of Sergey Naboko (1950-2020). In addition to original research contributions covering the vast areas of interest of Sergey Naboko, it includes personal reminiscences and comments on the works and legacy of Sergey Naboko’s scientific achievements. Areas from complex analysis to operator theory, especially, spectral theory, are covered, and the papers will inspire current and future researchers in these areas.
Inverse Linear Problems On Hilbert Space And Their Krylov Solvability
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Author : Noè Angelo Caruso
language : en
Publisher: Springer Nature
Release Date : 2022-02-10
Inverse Linear Problems On Hilbert Space And Their Krylov Solvability written by Noè Angelo Caruso and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-10 with Mathematics categories.
This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector f in a Hilbert space H, a linear operator A acting on H, and a vector g in H satisfying Af=g, one is interested in approximating f by finite linear combinations of g, Ag, A2g, A3g, ... The closed subspace generated by the latter vectors is called the Krylov subspace of H generated by g and A. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text. After giving a broad introduction to the subject, examples and counterexamples of Krylov-solvable and non-solvable inverse problems are provided, together with results on uniqueness of solutions, classes of operators inducing Krylov-solvable inverse problems, and the behaviour of Krylov subspaces under small perturbations. An appendix collects material on weaker convergence phenomena in general projection methods. This subject of this book lies at the boundary of functional analysis/operator theory and numerical analysis/approximation theory and will be of interest to graduate students and researchers in any of these fields.
A Mathematical Primer On Quantum Mechanics
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Author : Alessandro Teta
language : en
Publisher: Springer
Release Date : 2018-04-17
A Mathematical Primer On Quantum Mechanics written by Alessandro Teta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-17 with Science categories.
This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.
Methods For Solving Mathematical Physics Problems
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Author : Valeriĭ Ivanovich Agoshkov
language : en
Publisher: Cambridge Int Science Publishing
Release Date : 2006
Methods For Solving Mathematical Physics Problems written by Valeriĭ Ivanovich Agoshkov and has been published by Cambridge Int Science Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Science categories.
The aim of the book is to present to a wide range of readers (students, postgraduates, scientists, engineers, etc.) basic information on one of the directions of mathematics, methods for solving mathematical physics problems. The authors have tried to select for the book methods that have become classical and generally accepted. However, some of the current versions of these methods may be missing from the book because they require special knowledge. The book is of the handbook-teaching type. On the one hand, the book describes the main definitions, the concepts of the examined methods and approaches used in them, and also the results and claims obtained in every specific case. On the other hand, proofs of the majority of these results are not presented and they are given only in the simplest (methodological) cases. Another special feature of the book is the inclusion of many examples of application of the methods for solving specific mathematical physics problems of applied nature used in various areas of science and social activity, such as power engineering, environmental protection, hydrodynamics, elasticity theory, etc. This should provide additional information on possible applications of these methods. To provide complete information, the book includes a chapter dealing with the main problems of mathematical physics, together with the results obtained in functional analysis and boundary-value theory for equations with partial derivatives.
Lectures On Geometric Methods In Mathematical Physics
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Author : Jerrold E. Marsden
language : en
Publisher: SIAM
Release Date : 1981-01-01
Lectures On Geometric Methods In Mathematical Physics written by Jerrold E. Marsden and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-01 with Science categories.
A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation and Hamiltonian systems in diverse applications are explored.