Non-selfadjoint operators in quantum physics : mathematical aspects /
A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring cov...
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| Other Authors: | , , , |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Hoboken, New Jersey :
John Wiley & Sons,
2015.
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| Subjects: | |
| Online Access: | CONNECT |
MARC
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| 245 | 0 | 0 | |a Non-selfadjoint operators in quantum physics : |b mathematical aspects / |c editors: Fabio Bagarello, Jean Pierre Gazeau, Franciszek Hugon Szafraniec, Miloslav Znojil. |
| 264 | 1 | |a Hoboken, New Jersey : |b John Wiley & Sons, |c 2015. | |
| 264 | 4 | |c ©2015 | |
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| 505 | 0 | |6 880-01 |a Ideas and trends / Miloslav Znojil -- Operators of the quantum harmonic oscillator and its relatives / Franciszek Hugon Szafraniec -- Deformed canonical (anti) commutation relations and non selfadjoint Hamiltonians / Fabio Bagarello -- Reality of the spectrum and existence of PT-symmetric phase transitions / Emanuela Caliceti and Sandro Graffi -- Elements of spectral theory without the spectral theorem / David Krejčiřík and Petr Siegl -- PT-symmetric operators in quantum mechanics: Krein spaces methods / Sergio Albeverio and Sergii Kuzhel -- Metric operators, generalized hermiticity and lattices of Hilbert spaces / Jean-Pierre Antoine and Camillo Trapani. | |
| 588 | 0 | |a Print version record and CIP data provided by publisher. | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features: Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level. | ||
| 520 | 8 | |a And/or PhD-level text for courses on quantum mechanics and mathematical models in physics. | |
| 650 | 0 | |a Nonselfadjoint operators. | |
| 650 | 0 | |a Spectral theory (Mathematics) | |
| 650 | 0 | |a Quantum theory |x Mathematics. | |
| 650 | 0 | |a Hilbert space. | |
| 700 | 1 | |a Bagarello, Fabio, |d 1964- |e editor. | |
| 700 | 1 | |a Gazeau, Jean-Pierre, |e editor. | |
| 700 | 1 | |a Szafraniec, Franciszek Hugon, |e editor. | |
| 700 | 1 | |a Znojil, M. |q (Miloslav), |e editor. | |
| 730 | 0 | |a WILEYEBA | |
| 776 | 0 | 8 | |i Print version: |t Non-selfadjoint operators in quantum physics. |d Hoboken, New Jersey : John Wiley & Sons, 2015 |z 9781118855287 |w (DLC) 2014048325 |
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| 880 | 0 | |6 505-00 |a Cover -- Title Page -- Copyright -- Dedication -- Contributors -- Contents in Brief -- Contents -- Preface -- Acronyms -- Glossary -- Symbols -- Introduction -- References -- Chapter 1 Non-Self-Adjoint Operators in Quantum Physics: Ideas, People, and Trends -- 1.1 The Challenge of Non-Hermiticity in Quantum Physics -- 1.1.1 A Few Quantum Physics' Anniversaries, for Introduction -- 1.1.2 Dozen Years of Conferences Dedicated to Pseudo-Hermiticity -- 1.2 A Periodization of the Recent History of Study of Non-Self-Adjoint Operators in Quantum Physics -- 1.2.1 The Years of Crises -- 1.2.2 The Periods of Growth -- 1.3 Main Message: New Classes of Quantum Bound States -- 1.3.1 Real Energies via Non-Hermitian Hamiltonians -- 1.3.2 Analytic and Algebraic Constructions -- 1.3.3 Qualitative Innovations of Phenomenological Quantum Models -- 1.4 Probabilistic Interpretation of the New Models -- 1.4.1 Variational Constructions -- 1.4.2 Non-Dirac Hilbert-Space Metrics Θ ≠ I -- 1.5 Innovations in Mathematical Physics -- 1.5.1 Simplified Schrödinger Equations -- 1.5.2 Nonconservative Systems and Time-Dependent Dyson Mappings -- 1.6 Scylla of Nonlocality or Charybdis of Nonunitarity-- 1.6.1 Scattering Theory -- 1.6.2 Giving up the Locality of Interaction -- 1.6.3 The Threat of the Loss of Unitarity -- 1.7 Trends -- 1.7.1 Giving Up Metrics -- 1.7.2 Giving Up Unitarity -- 1.7.3 Giving Up Quantization -- References -- Chapter 2 Operators of the Quantum Harmonic Oscillator and Its Relatives -- 2.1 Introducing to Unbounded Hilbert Space Operators -- 2.1.1 How to Understand an Unbounded Operator -- 2.1.2 Very Basic Notions and Facts -- 2.1.3 Subnormal Operators -- 2.1.4 Operators in the Reproducing Kernel Hilbert Space -- 2.2 Commutation Relations. | |
| 880 | 8 | |6 505-01 |a 2.2.1 The Commutation Relation of the Quantum Harmonic Oscillator -- 2.2.2 Duality -- 2.3 The q-Oscillators -- 2.3.1 Spatial Interpretation of (q-o) -- 2.3.2 Subnormality in the q-Oscillator -- 2.4 Back to "Hermicity"-A Way to See It -- Concluding Remarks -- References -- Chapter 3 Deformed Canonical (Anti- )Commutation Relations and Non-Self-Adjoint Hamiltonians -- 3.1 Introduction -- 3.2 The Mathematics of D-PBs -- 3.2.1 Some Preliminary Results on Bases and Complete Sets -- 3.2.2 Back to D-PBs -- 3.2.3 The Operators Sφ and Sψ -- 3.2.4 Θ-Conjugate Operators for D-Quasi Bases -- 3.2.5 D-PBs versus Bosons -- 3.3 D-PBs in Quantum Mechanics -- 3.3.1 The Harmonic Oscillator: Losing Self-adjointness -- 3.3.2 A Two-dimensional Model in a Flat noncommutative space -- 3.4 Other Appearances of D-PBs in Quantum Mechanics -- 3.4.1 The Extended Quantum Harmonic Oscillator -- 3.4.2 The Swanson Model -- 3.4.3 Generalized Landau Levels -- 3.4.4 An Example by Bender and Jones -- 3.4.5 A Perturbed Harmonic Oscillator in d=2 -- 3.4.6 A Last Perturbative Example -- 3.5 A Much Simpler Case: Pseudo-Fermions -- 3.5.1 A First Example from the Literature -- 3.5.2 More Examples from the Literature -- 3.6 A Possible Extension: Nonlinear D-PBs -- 3.7 Conclusions -- 3.8 Acknowledgments -- References -- Chapter 4 Criteria for the Reality of the Spectrum of PT-Symmetric Schrödinger Operators and for the Existence of PT-Symmetric Phase Transitions -- 4.1 Introduction -- 4.2 Perturbation Theory and Global Control of the Spectrum -- 4.3 One-Dimensional PT-Symmetric Hamiltonians: Criteria for the Reality of the Spectrum -- 4.4 PT-Symmetric Periodic Schrödinger Operators with Real Spectrum -- 4.5 An Example of PT-Symmetric Phase Transition -- 4.5.1 Holomorphy and Borel Summability at Infinity. | |
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