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Hilbert space operators in quantum physics:

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Bibliographische Detailangaben
Beteiligte Personen:	Blank, Jiří 1939-1990 (VerfasserIn), Exner, Pavel 1946- (VerfasserIn), Havlíček, Miroslav (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	[New York, NY] Springer 2008
Ausgabe:	2. ed.
Schriftenreihe:	Theoretical and Mathematical Physics
Schlagwörter:	Mathematische Physik Quantentheorie Hilbert space Mathematical physics Quantum theory Hilbert-Raum
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017151690&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XVII, 664 S.
ISBN:	9781402088698

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Datensatz im Suchindex

DE-BY-TUM_call_number	0102 PHY 020f 2009 A 2417(2)
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adam_text	Contents Preface to the second edition vii Preface ix 1 Some notions from functional analysis 1 1.1 Vector and normed spaces ........................ 1 1.2 Metric and topological spaces ...................... 5 1.3 Compactness ............................... 10 1.4 Topological vector spaces ......................... 13 1.5 Banach spaces and operators on them .................. 15 1.6 The principle of uniform boundedness .................. 23 1.7 Spectra of closed linear operators .................... 25 Notes to Chapter 1............................... 29 Problems .................................... 32 2 Hubert spaces 41 2.1 The geometry of Hilbert spaces ..................... 41 2.2 Examples ................................. 45 2.3 Direct sums of Hilbert spaces ...................... 50 2.4 Tensor products .............................. 54 Notes to Chapter 2............................... 56 Problems .................................... 59 3 Bounded operators 63 3.1 Basic notions ............................... 63 3.2 Hermitean operators ........................... 67 3.3 Unitary and isometric operators ..................... 72 3.4 Spectra of bounded normal operators .................. 74 3.5 Compact operators ............................ 77 3.6 Hilbert-Schmidt and trace-class operators ............... 81 Notes to Chapter 3............................... 87 Problems .................................... 88 xiii r Contents Unbounded operators 93 4.1 The adjoint ................................ 93 4.2 Closed operators ............................. 95 4.3 Normal operators. Self-adjointness ...................100 4.4 Reducibility. Unitary equivalence ....................105 4.5 Tensor products ..............................108 4.6 Quadratic forms .............................. HO 4.7 Self-adjoint extensions ..........................117 4.8 Ordinary differential operators ......................126 4.9 Self-adjoint extensions of differential operators .............133 Notes to Chapter 4...............................139 Problems ....................................142 Spectral theory 151 5.1 Projection-valued measures .......................151 5.2 Functional calculus ............................156 5.3 The spectral theorem ...........................165 5.4 Spectra of self-adjoint operators .....................171 5.5 Functions of self-adjoint operators ....................176 5.6 Analytic vectors ..............................183 5.7 Tensor products ..............................185 5.8 Spectral representation ..........................187 5.9 Groups of unitary operators .......................191 Notes to Chapter 5...............................195 Problems ....................................197 Operator sets and algebras 205 6.1 C* -algebras ................................205 6.2 GNS construction .............................208 6.3 W-algebras ................................213 6.4 Normal states on W-algebras ......................221 6.5 Commutative symmetric operator sets .................227 6.6 Complete sets of commuting operators .................232 6.7 Irreducibility. Functions of non-commuting operators .........235 6.8 Algebras of unbounded operators ....................239 Notes to Chapter 6...............................241 Problems ....................................246 States and observables 251 7.1 Basic postulates ..............................251 7.2 Simple examples .............................259 7.3 Mixed states ................................264 7.4 Supersełection rules ............................268 7.5 Compatibility ...............................273 Contents xv 7.6 The algebraic approach ..........................282 Notes to Chapter 7...............................285 Problems ....................................289 8 Position and momentum 293 8.1 Uncertainty relations ...........................293 8.2 The canonical commutation relations ..................299 8.3 The classical limit and quantization ...................306 Notes to Chapter 8...............................310 Problems ....................................313 9 Time evolution 317 9.1 The fundamental postulate ........................317 9.2 Pictures of motion ............................323 9.3 Two examples ...............................325 9.4 The Feynman integral ..........................330 9.5 Nonconservative systems .........................334 9.6 Unstable systems .............................340 Notes to Chapter 9...............................348 Problems ....................................354 10 Symmetries of quantum systems 357 10.1 Basic notions ...............................357 10.2 Some examples ..............................362 10.3 General space-time transformations ...................370 Notes to Chapter 10..............................373 Problems ....................................375 11 Composite systems 379 11.1 States and observables ..........................379 11.2 Reduced states ..............................383 11.3 Time evolution ..............................388 11.4 Identical particles .............................389 11.5 Separation of variables. Symmetries ...................392 Notes to Chapter 11 ..............................398 Problems ....................................400 12 The second quantization 403 12.1 Fock spaces ................................403 12.2 Creation and annihilation operators ...................408 12.3 Systems of noninteracting particles ...................413 Notes to Chapter 12..............................420 Problems ....................................423 xvj Contents 13 Axiomatization of quantum theory 425 13.1 Lattices of propositions ..........................425 13.2 States on proposition systems ......................430 13.3 Axioms for quantum field theory ....................434 Notes to Chapter 13..............................438 Problems ....................................441 14 Schrödinger operators 443 14.1 Self-adjointness ..............................443 14.2 The minimax principle. Analytic perturbations .............448 14.3 The discrete spectrum ..........................454 14.4 The essential spectrum ..........................462 14.5 Constrained motion ............................471 14.6 Point and contact interactions ......................474 Notes to Chapter 14..............................479 Problems ....................................486 15 Scattering theory 491 15.1 Basic notions ...............................491 15.2 Existence of wave operators .......................498 15.3 Potential scattering ............................506 15.4 A model of two-channel scattering ...................510 Notes to Chapter 15..............................521 Problems ....................................524 16 Quantum waveguides 527 16.1 Geometric effects in Dirichlet stripes ..................527 16.2 Point perturbations ............................532 16.3 Curved quantum layers ..........................539 16.4 Weak coupling ...............................547 Notes to Chapter 16..............................552 Problems ....................................555 17 Quantum graphs 561 17.1 Admissible Hamiltonians .........................561 17.2 Meaning of the vertex coupling .....................566 17.3 Spectral and scattering properties ....................570 17.4 Generalized graphs ............................579 17.5 Leaky graphs ...............................580 Notes to Chapter 17..............................587 Problems ....................................590 Contents xvii A Measure and integration 595 A.I Sets, mappings, relations .........................595 A.2 Measures and measurable functions ...................598 A.3 Integration .................................601 A.4 Complex measures ............................605 A.5 The Bochner integral ...........................607 В Some algebraic notions 609 B.I Involutive algebras ............................609 B.2 Banach algebras ..............................612 B.3 Lie algebras and Lie groups .......................614 References 617 List of symbols 647 Index 651
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author	Blank, Jiří 1939-1990 Exner, Pavel 1946- Havlíček, Miroslav
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discipline	Physik Mathematik Geographie
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spellingShingle	Blank, Jiří 1939-1990 Exner, Pavel 1946- Havlíček, Miroslav Hilbert space operators in quantum physics Mathematische Physik Quantentheorie Hilbert space Mathematical physics Quantum theory Quantentheorie (DE-588)4047992-4 gnd Hilbert-Raum (DE-588)4159850-7 gnd
subject_GND	(DE-588)4047992-4 (DE-588)4159850-7
title	Hilbert space operators in quantum physics
title_auth	Hilbert space operators in quantum physics
title_exact_search	Hilbert space operators in quantum physics
title_full	Hilbert space operators in quantum physics Jirí Blank ; Pavel Exner ; Miloslav Havlícek
title_fullStr	Hilbert space operators in quantum physics Jirí Blank ; Pavel Exner ; Miloslav Havlícek
title_full_unstemmed	Hilbert space operators in quantum physics Jirí Blank ; Pavel Exner ; Miloslav Havlícek
title_short	Hilbert space operators in quantum physics
title_sort	hilbert space operators in quantum physics
topic	Mathematische Physik Quantentheorie Hilbert space Mathematical physics Quantum theory Quantentheorie (DE-588)4047992-4 gnd Hilbert-Raum (DE-588)4159850-7 gnd
topic_facet	Mathematische Physik Quantentheorie Hilbert space Mathematical physics Quantum theory Hilbert-Raum
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017151690&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT blankjiri hilbertspaceoperatorsinquantumphysics AT exnerpavel hilbertspaceoperatorsinquantumphysics AT havlicekmiroslav hilbertspaceoperatorsinquantumphysics

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