Intermediate Spectral Theory And Quantum Dynamics

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Intermediate Spectral Theory And Quantum Dynamics

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Author : César R. de Oliveira
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-30

Intermediate Spectral Theory And Quantum Dynamics written by César R. de Oliveira and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-30 with Science categories.

The spectral theory of linear operators plays a key role in the mathematical formulation of quantum theory. This textbook provides a concise and comprehensible introduction to the spectral theory of (unbounded) self-adjoint operators and its application in quantum dynamics. Many examples and exercises are included that focus on quantum mechanics.

Spectral Theory And Mathematical Physics

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Author : Pablo Miranda
language : en
Publisher: Springer Nature
Release Date : 2020-11-12

Spectral Theory And Mathematical Physics written by Pablo Miranda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-12 with Mathematics categories.

This proceedings volume contains peer-reviewed, selected papers and surveys presented at the conference Spectral Theory and Mathematical Physics (STMP) 2018 which was held in Santiago, Chile, at the Pontifical Catholic University of Chile in December 2018. The original works gathered in this volume reveal the state of the art in the area and reflect the intense cooperation between young researchers in spectral theoryand mathematical physics and established specialists in this field. The list of topics covered includes: eigenvalues and resonances for quantum Hamiltonians; spectral shift function and quantum scattering; spectral properties of random operators; magnetic quantum Hamiltonians; microlocal analysis and its applications in mathematical physics. This volume can be of interest both to senior researchers and graduate students pursuing new research topics in Mathematical Physics.

Spectral Analysis Of Quantum Hamiltonians

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Author : Rafael Benguria
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-30

Spectral Analysis Of Quantum Hamiltonians written by Rafael Benguria and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-30 with Mathematics categories.

This volume contains surveys as well as research articles broadly centered on spectral analysis. Topics range from spectral continuity for magnetic and pseudodifferential operators to localization in random media, from the stability of matter to properties of Aharonov-Bohm and Quantum Hall Hamiltonians, from waveguides and resonances to supersymmetric models and dissipative fermion systems. This is the first of a series of volumes reporting every two years on recent progress in spectral theory.​

Mathematical Concepts Of Quantum Mechanics

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Author : Stephen J. Gustafson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-24

Mathematical Concepts Of Quantum Mechanics written by Stephen J. Gustafson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-24 with Mathematics categories.

The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory.

Spectral Measures And Dynamics Typical Behaviors

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Author : Moacir Aloisio
language : en
Publisher: Springer Nature
Release Date : 2023-10-27

Spectral Measures And Dynamics Typical Behaviors written by Moacir Aloisio and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-27 with Science categories.

This book convenes and deepens generic results about spectral measures, many of them available so far in scattered literature. It starts with classic topics such as Wiener lemma, Strichartz inequality, and the basics of fractal dimensions of measures, progressing to more advanced material, some of them developed by the own authors. A fundamental concept to the mathematical theory of quantum mechanics, the spectral measure relates to the components of the quantum state concerning the energy levels of the Hamiltonian operator and, on the other hand, to the dynamics of such state. However, these correspondences are not immediate, with many nuances and subtleties discovered in recent years. A valuable example of such subtleties is found in the so-called “Wonderland theorem” first published by B. Simon in 1995. It shows that, for some metric space of self-adjoint operators, the set of operators whose spectral measures are singular continuous is a generic set (which, for some, is exotic). Recent works have revealed that, on top of singular continuity, there are other generic properties of spectral measures. These properties are usually associated with a number of different notions of generalized dimensions, upper and lower dimensions, with dynamical implications in quantum mechanics, ergodicity of dynamical systems, and evolution semigroups. All this opens ways to new and instigating avenues of research. Graduate students with a specific interest in the spectral properties of spectral measure are the primary target audience for this work, while researchers benefit from a selection of important results, many of them presented in the book format for the first time.

Mathematical Methods In Quantum Mechanics

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Author : Gerald Teschl
language : en
Publisher:
Release Date : 2009

Mathematical Methods In Quantum Mechanics written by Gerald Teschl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Quantum theory categories.

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.

Mystery Of Time The Asymmetry Of Time And Irreversibility In The Natural Processes

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Author : Alexander Leonidovich Kuzemsky
language : en
Publisher: World Scientific
Release Date : 2022-10-14

Mystery Of Time The Asymmetry Of Time And Irreversibility In The Natural Processes written by Alexander Leonidovich Kuzemsky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-14 with Science categories.

The book focuses on the study of the temporal behavior of complex many-particle systems. The phenomenon of time and its role in the temporal evolution of complex systems is a remaining mystery. The book presents the necessity of the interdisciplinary point of view regarding on the phenomenon of time.The aim of the present study is to summarize and formulate in a concise but clear form the trends and approaches to the concept of time from a broad interdisciplinary perspective exposing tersely the complementary approaches and theories of time in the context of thermodynamics, statistical physics, cosmology, theory of information, biology and biophysics, including the problem of time and aging. Various approaches to the problem show that time is an extraordinarily interdisciplinary and multifaceted underlying notion which plays an extremely important role in various natural complex processes.

Contact Interactions In Quantum Mechanics Theory Mathematical Aspects And Applications

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Author : Manuel Gadella
language : en
Publisher: Frontiers Media SA
Release Date : 2021-03-12

Contact Interactions In Quantum Mechanics Theory Mathematical Aspects And Applications written by Manuel Gadella and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-12 with Science categories.

A Comprehensive Guide To Advanced Quantum Mechanics

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Author : Sanjay Nair
language : en
Publisher: Educohack Press
Release Date : 2025-02-20

A Comprehensive Guide To Advanced Quantum Mechanics written by Sanjay Nair and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.

Embark on a journey into the captivating realm of quantum physics with our comprehensive guide, tailored for undergraduate students in the United States. Building upon the foundational principles of introductory quantum mechanics, our book delves into the deeper complexities and cutting-edge advancements of the quantum world. We cover a wide range of advanced quantum mechanics topics, equipping students with the theoretical framework and mathematical tools to understand and analyze complex quantum phenomena. From quantum field theory principles to the intricacies of quantum entanglement and decoherence, each chapter offers clear explanations and illustrative examples to help grasp key concepts. Emphasizing both theoretical understanding and practical application, our guide includes thought-provoking exercises and real-world examples that challenge students to deeply engage with the material. Through this rigorous yet accessible approach, students will expand their knowledge of quantum mechanics and develop valuable problem-solving skills essential for further study and research in physics. Whether pursuing a career in theoretical physics, quantum information science, or simply seeking to deepen their understanding of the quantum world, students will find our guide to be an invaluable resource that illuminates the complexities and wonders of one of the most fascinating fields in modern physics.