{"product_id":"nonselfadjoint-operators-in-quantum-physics-9781118855287","title":"NonSelfadjoint Operators in Quantum Physics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eA unique discussion of mathematical methods with applications to quantum mechanics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eNon-Selfadjoint Operators in Quantum Physics: Mathematical Aspects \u003c\/i\u003epresents 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:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eChapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers whil\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003eAcronyms xix\u003c\/p\u003e \u003cp\u003eGlossary xxi\u003c\/p\u003e \u003cp\u003eSymbols xxiii\u003c\/p\u003e \u003cp\u003eIntroduction 1\u003cbr\u003e\u003ci\u003eF. Bagarello, J.P. Gazeau, F. Szafraniec, and M. Znojil\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eReferences 5\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Non-Self-Adjoint Operators in Quantum Physics: Ideas, People, and Trends 7\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eMiloslav Znojil\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1 The Challenge of Non-Hermiticity in Quantum Physics 7\u003c\/p\u003e \u003cp\u003e1.2 A Periodization of the Recent History of Study of Non-Self-Adjoint Operators in Quantum Physics 11\u003c\/p\u003e \u003cp\u003e1.3 Main Message: New Classes of Quantum Bound States 18\u003c\/p\u003e \u003cp\u003e1.4 Probabilistic Interpretation of the New Models 29\u003c\/p\u003e \u003cp\u003e1.5 Innovations in Mathematical Physics 34\u003c\/p\u003e \u003cp\u003e1.6 Scylla of Nonlocality or Charybdis of Nonunitarity? 37\u003c\/p\u003e \u003cp\u003e1.7 Trends 45\u003c\/p\u003e \u003cp\u003eReferences 50\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Operators of the Quantum Harmonic Oscillator and Its Relatives 59\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eFranciszek Hugon Szafraniec\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introducing to Unbounded Hilbert Space Operators 60\u003c\/p\u003e \u003cp\u003e2.2 Commutation Relations 88\u003c\/p\u003e \u003cp\u003e2.3 The q–Oscillators 106\u003c\/p\u003e \u003cp\u003e2.4 Back to “Hermicity”—A Way to See It 113\u003c\/p\u003e \u003cp\u003eConcluding Remarks 115\u003c\/p\u003e \u003cp\u003eReferences 115\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Deformed Canonical (Anti-)Commutation Relations and Non-Self-Adjoint Hamiltonians 121\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eFabio Bagarello\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 121\u003c\/p\u003e \u003cp\u003e3.2 The Mathematics of \u003ci\u003eD\u003c\/i\u003e-PBs 123\u003c\/p\u003e \u003cp\u003e3.3 \u003ci\u003eD\u003c\/i\u003e-PBs in Quantum Mechanics 145\u003c\/p\u003e \u003cp\u003e3.4 Other Appearances of \u003ci\u003eD\u003c\/i\u003e-PBs in Quantum Mechanics 158\u003c\/p\u003e \u003cp\u003e3.5 A Much Simpler Case: Pseudo-Fermions 174\u003c\/p\u003e \u003cp\u003e3.6 A Possible Extension: Nonlinear \u003ci\u003eD\u003c\/i\u003e-PBs 182\u003c\/p\u003e \u003cp\u003e3.7 Conclusions 184\u003c\/p\u003e \u003cp\u003e3.8 Acknowledgments 185\u003c\/p\u003e \u003cp\u003eReferences 185\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Criteria for the Reality of the Spectrum of \u003ci\u003ePT\u003c\/i\u003e -Symmetric Schrödinger Operators and for the Existence of \u003ci\u003ePT\u003c\/i\u003e -Symmetric Phase Transitions 189\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eEmanuela Caliceti and Sandro Graffi\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 189\u003c\/p\u003e \u003cp\u003e4.2 Perturbation Theory and Global Control of the Spectrum 191\u003c\/p\u003e \u003cp\u003e4.3 One-Dimensional \u003ci\u003ePT\u003c\/i\u003e -Symmetric Hamiltonians: Criteria for the Reality of the Spectrum 194\u003c\/p\u003e \u003cp\u003e4.4 \u003ci\u003ePT\u003c\/i\u003e -Symmetric Periodic Schrödinger Operators with Real Spectrum 200\u003c\/p\u003e \u003cp\u003e4.5 An Example of \u003ci\u003ePT\u003c\/i\u003e -Symmetric Phase Transition 206\u003c\/p\u003e \u003cp\u003e4.6 The Method of the Quantum Normal Form 219\u003c\/p\u003e \u003cp\u003eAppendix: Moyal Brackets and theWeyl Quantization 232\u003c\/p\u003e \u003cp\u003eA.1 Moyal Brackets 232\u003c\/p\u003e \u003cp\u003eA.2 The Weyl Quantization 236\u003c\/p\u003e \u003cp\u003eReferences 238\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Elements of Spectral Theory without the Spectral Theorem 241\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eDavid Krejèiøík and Petr Siegl\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 241\u003c\/p\u003e \u003cp\u003e5.2 Closed Operators in Hilbert Spaces 242\u003c\/p\u003e \u003cp\u003e5.3 How to Whip Up a Closed Operator 257\u003c\/p\u003e \u003cp\u003e5.4 Compactness and a Spectral Life Without It 266\u003c\/p\u003e \u003cp\u003e5.5 Similarity to Normal Operators 273\u003c\/p\u003e \u003cp\u003e5.6 Pseudospectra 281\u003c\/p\u003e \u003cp\u003eReferences 288\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 \u003ci\u003ePT\u003c\/i\u003e -Symmetric Operators in Quantum Mechanics: Krein Spaces Methods 293\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eSergio Albeverio and Sergii Kuzhel\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 293\u003c\/p\u003e \u003cp\u003e6.2 Elements of the Krein Spaces Theory 295\u003c\/p\u003e \u003cp\u003e6.3 Self-Adjoint Operators in Krein Spaces 304\u003c\/p\u003e \u003cp\u003e6.4 Elements of \u003ci\u003ePT\u003c\/i\u003e -Symmetric Operators Theory 320\u003c\/p\u003e \u003cp\u003eReferences 340\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Metric Operators, Generalized Hermiticity and Lattices of Hilbert Spaces 345\u003cbr\u003e\u003c\/b\u003e\u003ci\u003eJean-Pierre Antoine and Camillo Trapani\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 345\u003c\/p\u003e \u003cp\u003e7.2 Some Terminology 347\u003c\/p\u003e \u003cp\u003e7.3 Similar and Quasi-Similar Operators 349\u003c\/p\u003e \u003cp\u003e7.4 The Lattice Generated by a Single Metric Operator 362\u003c\/p\u003e \u003cp\u003e7.5 Quasi-Hermitian Operators 367\u003c\/p\u003e \u003cp\u003e7.6 The LHS Generated by Metric Operators 380\u003c\/p\u003e \u003cp\u003e7.7 Similarity for PIP-Space Operators 382\u003c\/p\u003e \u003cp\u003e7.8 The Case of Pseudo-Hermitian Hamiltonians 389\u003c\/p\u003e \u003cp\u003e7.9 Conclusion 392\u003c\/p\u003e \u003cp\u003eAppendix: Partial Inner Product Spaces 392\u003c\/p\u003e \u003cp\u003eA.1 PIP-Spaces and Indexed PIP-Spaces 392\u003c\/p\u003e \u003cp\u003eA.2 Operators on Indexed PIP-space S 395\u003c\/p\u003e \u003cp\u003eA.2.1 Symmetric Operators 396\u003c\/p\u003e \u003cp\u003eA.2.2 Regular Operators, Morphisms, and Projections 397\u003c\/p\u003e \u003cp\u003eReferences 399\u003c\/p\u003e \u003cp\u003eIndex 403\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406935630167,"sku":"9781118855287","price":93.57,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118855287.jpg?v=1730497612","url":"https:\/\/bookcurl.com\/products\/nonselfadjoint-operators-in-quantum-physics-9781118855287","provider":"Book Curl","version":"1.0","type":"link"}