Expansions In Eigenfunctions Of Selfadjoint Operators Selfadjoint Operators
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Expansions In Eigenfunctions Of Selfadjoint Operators
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Author : I͡Uriĭ Makarovich Berezanskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 1968
Expansions In Eigenfunctions Of Selfadjoint Operators written by I͡Uriĭ Makarovich Berezanskiĭ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Boundary value problems categories.
Expansions In Eigenfunctions Of Selfadjoint Operators
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Author :
language : en
Publisher:
Release Date : 1968
Expansions In Eigenfunctions Of Selfadjoint Operators written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Boundary value problems categories.
Spectral Methods In Infinite Dimensional Analysis 2 1995
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Author : I︠U︡riĭ Makarovich Berezanskiĭ
language : en
Publisher: Springer Science & Business Media
Release Date : 1995
Spectral Methods In Infinite Dimensional Analysis 2 1995 written by I︠U︡riĭ Makarovich Berezanskiĭ 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 1995 with Degree of freedom categories.
Expansions In Eigenfunctions Of Selfadjoint Operators Selfadjoint Operators
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Author : John Rose
language : en
Publisher:
Release Date : 1968
Expansions In Eigenfunctions Of Selfadjoint Operators Selfadjoint Operators written by John Rose and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Advanced Quantum Mechanics
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Author : RAINER DICK
language : en
Publisher: Springer
Release Date : 2016-07-01
Advanced Quantum Mechanics written by RAINER DICK and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-01 with Science categories.
In this updated and expanded second edition of a well-received and invaluable textbook, Prof. Dick emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. Advanced Quantum Mechanics, Materials and Photons can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. This second edition includes an additional 62 new problems as well as expanded sections on relativistic quantum fields and applications of quantum electrodynamics. Other special features include an introduction to Lagrangian field theory and an integrated discussion of transition amplitudes with discrete or continuous initial or final states. Once students have acquired an understanding of basic quantum mechanics and classical field theory, canonical field quantization is easy. Furthermore, the integrated discussion of transition amplitudes naturally leads to the notions of transition probabilities, decay rates, absorption cross sections and scattering cross sections, which are important for all experimental techniques that use photon probes.
Unbounded Self Adjoint Operators On Hilbert Space
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Author : Konrad Schmüdgen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-09
Unbounded Self Adjoint Operators On Hilbert Space written by Konrad Schmüdgen 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 2012-07-09 with Mathematics categories.
The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises. The main themes of the book are the following: - Spectral integrals and spectral decompositions of self-adjoint and normal operators - Perturbations of self-adjointness and of spectra of self-adjoint operators - Forms and operators - Self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extension
Non Self Adjoint Schr Dinger Operator With A Periodic Potential
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Author : Oktay Veliev
language : en
Publisher: Springer Nature
Release Date : 2025-08-03
Non Self Adjoint Schr Dinger Operator With A Periodic Potential written by Oktay Veliev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-03 with Science categories.
This book offers a comprehensive exploration of spectral theory for non-self-adjoint differential operators with complex-valued periodic coefficients, addressing one of the most challenging problems in mathematical physics and quantum mechanics: constructing spectral expansions in the absence of a general spectral theorem. It examines scalar and vector Schrödinger operators, including those with PT-symmetric periodic optical potentials, and extends these methodologies to higher-order operators with periodic matrix coefficients. The second edition significantly expands upon the first by introducing two new chapters that provide a complete description of the spectral theory of non-self-adjoint differential operators with periodic coefficients. The first of these new chapters focuses on the vector case, offering a detailed analysis of the spectral theory of non-self-adjoint Schrödinger operators with periodic matrix potentials. It thoroughly examines eigenvalues, eigenfunctions, and spectral expansions for systems of one-dimensional Schrödinger operators. The second chapter develops a comprehensive spectral theory for all ordinary differential operators, including higher-order and vector cases, with periodic coefficients. It also includes a complete classification of the spectrum for PT-symmetric periodic differential operators, making this edition the most comprehensive treatment of these topics to date. The book begins with foundational topics, including spectral theory for Schrödinger operators with complex-valued periodic potentials, and systematically advances to specialized cases such as the Mathieu–Schrödinger operator and PT-symmetric periodic systems. By progressively increasing the complexity, it provides a unified and accessible framework for students and researchers. The approaches developed here open new horizons for spectral analysis, particularly in the context of optics, quantum mechanics, and mathematical physics.
Expansions In Eigenfunctions Of Selfadjoint Operators
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Author :
language : en
Publisher:
Release Date : 1968
Expansions In Eigenfunctions Of Selfadjoint Operators written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Boundary value problems categories.
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.
Expansions In Eigenfunctions Of Selfadjoint Operators
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Author :
language : en
Publisher:
Release Date : 1968
Expansions In Eigenfunctions Of Selfadjoint Operators written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.