.

0 (hodnocen0 x )

BK

2nd ed.

Melville : AIP Press ; [Dordrecht] : Springer, c2008

xvii, 664 s. ; 24 cm

ISBN 978-1-4020-8869-8 (váz.)

Theoretical and mathematical physics, ISSN 1864-5879

Obsahuje bibliografii na s. 617-646 a rejstřík

000249736

Contents // Preface to the second edition Preface // 1 Some notions from functional analysis // 1.1 Vector and normed spaces... // 1.2 Metric and topological spaces... // 1.3 Compactness ... // 1.4 Topological vector spaces... // 1.5 Banach spaces and operators on them . . . // 1.6 The principle of uniform boundedness . . . // 1.7 Spectra of closed linear operators... // Notes to Chapter 1... // Problems ... // 2 Hilbert spaces // 2.1 The geometry of Hilbert spaces... // 2.2 Examples... // 2.3 Direct sums of Hilbert spaces... // 2.4 Tensor products... // Notes to Chapter 2... // Problems ... // 3 Bounded operators // 3.1 Basic notions... // 3.2 Hermitean operators... // 3.3 Unitary and isometric operators... // 3.4 Spectra of bounded normal operators . . . // 3.5 Compact operators... // 3.6 Hilbert-Schmidt and trace-class operators // Notes to Chapter 3... // Problems ... // xiii // vii // ix // 1 // 1 // 5 // 10 // 13 // 15 // 23 // 25 // 29 // 32 // 41 // 41 // 45 // 50 // 54 // 56 // 59 // 63 // 63 // 67 // 72 // 74 // 77 // 81 // 87 // 88 // XIV // Contents // 4 Unbounded operators 93 // 4.1 The adjoint...93 // 4.2 Closed operators ...95 // 4.3 Normal operators. Self-adjoint ness ...100 // 4.4 Reducibility. Unitary equivalence...105 // 4.5 Tensor products...108 // 4.6 Quadratic forms...110 // 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

// 5 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 // 6 Operator sets and algebras 205 // 6.1 C*-algebras...205 // 6.2 GNS construction...208 // 6.3 VF*-algebras...213 // 6.4 Normal states on tF*-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 // 7 States and observables 251 // 7.1 Basic postulates...251 // 7.2 Simple examples ...259 // 7.3 Mixed states...264 // 7.4 Superselection 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 // XVI // 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 // A Measure and integration // A.l Sets, mappings, relations... // A.2 Measures and measurable functions // A.3 Integration... // A.4 Complex measures... // A. 5 The Bodmer integral... // ? Some algebraic notions // B. l Involutive algebras... // B.2 Banach algebras... // B.3 Lie algebras and Lie groups . . . . // References // List of symbols // Index // XVI1 // 595 // 595 // 598 // 601 // 605 // 607 // 609 // 609 // 612 // 614 // 617 // 647 // 651