Quantum Physics:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Weinheim
Wiley-VCH
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| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Erscheint: 13. Oktober 2010 |
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
PREFACE X//I
1 ORIGIN OF MAIN QUANTUM CONCEPTS 1 .1 LIGHT: WAVES OR PARTICLES? / .2
PLANCK CONSTANT. BEGINNING OF THE QUANTUM ERA .3 PHOTONS J
.4 SPECTROSCOPY AND STABILITY OF ATOMS 5 .5 BOHR POSTULATES 6
.6 HYDROGEN ATOM 9
.7 CORRESPONDENCE PRINCIPLE 15 .8 SPATIAL QUANTIZATION IS
.9 SPIN 20
.10 DE BROGUE WAVES 21
2 WAVE FUNCTION AND THE SIMPLEST PROBLEMS 25 2.1 FREE MOTION 25
2.2 PROBABILITY DENSITY AND CURRENT 26 2.3 SUPERPOSITION PRINCIPLE AND
UNCERTAINTY 29 2.4 POTENTIAL WALL JO
2.5 POTENTIAL BARRIER 31
2.6 BARRIER PENETRATION 35 2.7 TUNNELING 36
3 BOUND SUTES 43
3.1 POTENTIAL BOX 43
3.2 ORTHOGONALITY AND COMPLETENESS 45 3.3 DELTA-FUNCTION* 46 3.4 TIME
EVOLUTION 49
3.5 SHALLOW WELL AND QUANTUM HALO 52 3.6 RESONANCES 59
3.7 LEVEL DENSITY 60
3.8 PERIODIC BOUNDARY CONDITIONS 62 3.9 COUNTING LEVELS IN A SMOOTH
POTENTIAL 63
QUANTUM PHY-ICS, VDWNE ): FROM BASICS TO SYMMETRIES AND PERTURBATIONS.
VLADIMIR ZELCVINSKY COPYRIGHT 2011 WILEY-VCH VERLAGGMBH & CO. KGAA,
WEINHEIM ISBN: 978-3-527-4O979-2
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1002408407
DIGITALISIERT DURCH
IMAGE 2
VI I CONTENTS
4 DYNAMICAL VARIABLES 67
4.1 MOMENTUM REPRESENTATION 67 4.2 INTRODUCING OPERATORS 70 4.3
COMMUTATORS 72 4.4 EIGENFUNCTIONS AND EIGENVALUES 74 4.5 MOMENTUM AS A
TRANSLATION GENERATOR 75 4.6 INTRODUCTION TO GROUPS* 78 4.7 ORBITAL
MOMENTUM AS A ROTATION GENERATOR 79 4.8 TRANSFORMATION OF OPERATORS 81
5 UNCERTAINTY RELATIONS 85 5.1 UNCERTAINTY IN WAVE MECHANICS 85 5.2
SIMPLE EXAMPLES 87 5.3 COMPLEMENTARITY AND PROBABILITY 91 5.4 WAVE
PACKET: PROPAGATION 94
5.5 SPREADING OF A WAVE PACKET 96 5.6 ESTIMATES WITH UNCERTAINTY
RELATIONS 100 5.7 CLASSIFICATION OF MOLECULAR EXCITATIONS 104 5.8 LEVEL
WIDTH 107 5.9 LINE WIDTH AND MOESSBAUER EFFECT 109
5.10 VIRTUAL PROCESSES AND RELATIVISTIC EFFECTS 112 5.11 SPATIAL
QUANTIZATION REVISITED 114
6 HUBERT SPACE AND OPERATORS 119 6.1 PROBABILITY AMPLITUDE 119 6.2
SUPERPOSITION AND INTERFERENCE 120 6.3 STATE VECTORS 123 6.4 GEOMETRY OF
HUBERT SPACE* 124 6.5 LINEAR OPERATORS* 128 6.6 HERMITIAN OPERATORS* 130
6.7 PROPERTIES OF HERMITIAN OPERATORS* I32
6.8 DIAGONALIZATION* 134 6.9 BASIS TRANSFORMATIONS* I36 6.10 CONTINUOUS
TRANSFORMATIONS AND GENERATORS* 138 6.11 PROJECTION OPERATORS* 140 6.12
OPERATORS OF OBSERVABLES 142 6.13 SIMULTANEOUS MEASURABILITY 144
6.14 QUANTIFYING UNCERTAINTY RELATIONS 146
7 QUANTUM DYNAMICS 153 7.1 HAMILTONIAN AND SCHROEDINGER EQUATION 153 7.2
SINGLE-PARTICLE HAMILTONIAN 155 7.3 CONTINUITY EQUATION 261
7.4 WIGNER DISTRIBUTION 165 7.5 HEISENBERG PICTURE 167 7.6 OPERATOR
DYNAMICS 168
IMAGE 3
CONTENTS I VIL
7.7 VIRIAL THEOREM 171
7.8 SURVIVAL PROBABILITY 173 7.9 SUM RULES 174
7.10 CONSERVATION LAWS 178 7.11 PATH INTEGRAL FORMULATION 180 7.12
RELATION TO CLASSICAL MECHANICS 183
7.13 BACK TO THE SCHROEDINGER PICTURE 184
8 DISCRETE SYMMETRIES 187 8.1 TIME-REVERSAL INVARIANCE 187 8.2
TIME-REVERSAL TRANSFORMATION OF OPERATORS 189 8.3 INVERSION AND PARITY
191 8.4 SCALARS AND PSEUDOSCALARS, VECTORS AND PSEUDOVECTORS 192 8.5
PARITY CONSERVATION 193 8.6 SYMMETRY OF A CRYSTAL LATTICE 197 8.7
QUASIMOMENTUM AND BLOCH FUNCTIONS 198 8.8 ENERGY BANDS 202
8.9 SYMMETRY OF MOLECULES 203 8.10 MORE GROUP THEORY: CONJUGATE CLASSES*
206 8.11 GROUP REPRESENTATIONS* 207 8.12 ORTHOGONALITY AND COMPLETENESS*
209 8.13 CHARACTERS* 212
9 ONE-DIMENSIONAL MOTION: CONTINUUM 217 9.1 EIGENVALUE PROBLEM 217 9.2
CONTINUOUS SPECTRUM 218 9.3 DEGENERACY IN THE CONTINUUM 221
9.4 TRANSFER MATRIX 224
9.5 DELAY TIME 225
9.6 UNIFORM FIELD 228
9.7 AIRY AND BESSEL FUNCTIONS* 229 9.8 ASYMPTOTIC BEHAVIOR* 232 9.9
ASYMPTOTICS OF THE AIRY FUNCTION* 234 9.10 GREEN FUNCTION FOR
ONE-DIMENSIONAL SCATTERING 237 9.11 POTENTIAL AS PERTURBATION 241 9.12
QUASISTATIONARY STATES 244
10 VARIATIONAL APPROACH AND DIAGONALIZATION 247 10.1 VARIATIONAL
PRINCIPLE 247 10.2 DIRECT VARIATIONAL METHOD 249 10.3 DIAGONALIZATION IN
A TRUNCATED BASIS 251
10.4 TWO-STATE SYSTEM 252 10.5 LEVEL REPULSION AND AVOIDED CROSSING 254
10.6 TIME EVOLUTION OF A TWO-STATE SYSTEM 257 10.7 BRIGHT STATE AND
FRAGMENTATION 259 10.8 COLLECTIVE STATES 261
IMAGE 4
VIII I CONTENTS
10.9 LANCZOS ALGORITHM 265
11 DISCRETE SPECTRUM AND HARMONIC OSCILLATOR 267 11.1 ONE-DIMENSIONAL
BOUND STATES 267 11.2 LINEAR HARMONIC OSCILLATOR 269 11.3 HERMITE
POLYNOMIALS* 275
11.4 HARMONIC OSCILLATOR IN PLANE: SEPARATION OF VARIABLES 278 11.5
ISOTROPIE OSCILLATOR 280 11.6 SOLVING THE PROBLEM IN POLAR COORDINATES
282 11.7 LADDER CONSTRUCTION 285
11.8 CREATION AND ANNIHILATION OPERATORS 286 11.9 OPERATOR SOLUTION FOR
THE HARMONIC OSCILLATOR 288
12 COHERENT AND SQUEEZED STATES 293 12.1 INTRODUCING COHERENT STATES 293
12.2 DISPLACEMENTS IN THE PHASE PLANE 294 12.3 PROPERTIES OF COHERENT
STATES 296 12.4 COHERENT STATES OF THE HARMONIC OSCILLATOR 298 12.5
LINEAR SOURCE 299 12.6 SEMICLASSICAL LIMIT, NUMBER OF QUANTA AND THE
PHASE 302
12.7 PAIRWISE SOURCE 304 12.8 SQUEEZED STATES 307 12.9 MORE ABOUT
SQUEEZED STATES 320
13 INTRODUCING MAGNETIC FIELD 325 13.1 MAGNETIC FIELD IN CLASSICAL
MECHANICS 315 13.2 QUANTUM FORMULATION AND GAUGE INVARIANCE 317 13.3 ARE
ELECTROMAGNETIC POTENTIALS OBSERVABLE? 320 13.4 LANDAU LEVELS: ENERGY
SPECTRUM 322 13.5 LANDAU LEVELS: DEGENERACY AND WAVE FUNCTIONS 323 13.6
QUANTUM HALL EFFECT 327 13.7 ARBITRARY DISPERSION LAW 332 13.8 SYMMETRIC
GAUGE 335 13.9 COHERENT STATES IN THE MAGNETIC FIELD 336
14 MACROSCOPIC QUANTUM COHERENCE 339 14.1 IDEAS OF MACROSCOPIC COHERENCE
339 14.2 MACROSCOPIC WAVE FUNCTION 340 14.3 HYDRODYNAMIC DESCRIPTION 342
14.4 DYNAMICS OF THE MACROSCOPIC COHERENT STATE 344 14.5 JOSEPHSON
EFFECTS 346 14.6 QUANTIZATION OF CIRCULATION AND QUANTUM VORTICES 349
14.7 MAGNETIC FLUXOID QUANTIZATION AND LONDON ELECTRODYNAMICS 353
15 SEMICLASSICAL (WKB) APPROXIMATION 357 15.1 HEURISTIC INTRODUCTION 357
15.2 SEMICLASSICAL APPROXIMATION 360
IMAGE 5
CONTENTS IIX
15.3 ASYMPTOTIC EXPANSION 363
15.4 STATIONARY PHASE 364 15.5 MATCHING CONDITIONS 365 15.6
BOHR-SOMMERFELD QUANTIZATION 369 15.7 SEMICLASSICAL MATRIX ELEMENTS 372
15.8 SOLUTIONS IN THE COMPLEX PLANE* 373 15.9 GOING AROUND THE COMPLEX
PLANE* 376 15.10 CONNECTION FORMULAE REVISITED* 378 15.11 CLOSE TURNING
POINTS* 379 15.12 PATH INTEGRAL APPROACH 383
16 ANGULAR MOMENTUM AND SPHERICAL FUNCTIONS 387 16.1 ANGULAR MOMENTUM AS
A GENERATOR OF ROTATIONS 387 16.2 SPIN 389
16.3 ANGULAR MOMENTUM MULTIPLETS 390 16.4 MATRIX ELEMENTS OF ANGULAR
MOMENTUM 396 16.5 REALIZATION OF THE ALGEBRA FOR ORBITAL MOMENTUM 399
16.6 CONSTRUCTING A SET OF SPHERICAL FUNCTIONS* 401
16.7 SIMPLEST PROPERTIES OF SPHERICAL FUNCTIONS* 403 16.8 SCALARS AND
VECTORS* 404 16.9 SECOND RANK TENSORS* 408 16.10 SPHERICAL FUNCTIONS AND
LEGENDRE POLYNOMIALS* 420 16.11 ANGULAR MOMENTUM IN AN EXTERNAL FIELD
414
17 MOTION IN A CENTRAL FIELD 417 17.1 REDUCTION TO THE ONE-BODY PROBLEM
417 17.2 SEPARATION OF ANGULAR VARIABLES 420
17.3 RADIAL PART OF THE SCHROEDINGER EQUATION 422 17.4 FREE MOTION 426
17.5 PLANE AND SPHERICAL WAVES 430 17.6 SPHERICAL WELL 432
17.7 SHORT-RANGE POTENTIAL 435 17.8 ADDING THE SECOND CENTER 436 17.9
THREE-DIMENSIONAL HARMONIC OSCILLATOR 439
18 HYDROGEN ATOM 445 18.1 BOUND STATES 445 18.2 GROUND STATE 447
18.3 DISCRETE SPECTRUM 450 18.4 OPERATOR SOLUTION 458 18.5 ON THE WAY TO
PRECISION SPECTROSCOPY 460 18.6 SOLUTION IN PARABOLIC COORDINATES* 462
18.7 CONTINUUM STATES 463
19 STATIONARY PERTURBATIONS 469 19.1 INTRODUCTION 469 19.2 PERTURBATION
THEORY WITH NO DEGENERACY 470
IMAGE 6
X I CONTENTS
19.3 CONVERGENCE 474
19.4 CASE OF CLOSE LEVELS 477 19.5 ADIABATIC APPROXIMATION 478 19.6
MOLECULAR ION OF HYDROGEN 482 19.7 INTERACTIONS OF ATOMS AT LARGE
DISTANCES 486
20 SPIN 1/2 489
20.1 SU(2) GROUP 489 20.2 SPIN 1/2: ALGEBRA 490 20.3 SPINORS 494 20.4
MAGNETIC RESONANCE 499 20.5 TIME-REVERSAL TRANSFORMATION AND KRAMERS
THEOREM 501 20.6 TIME-CONJUGATE STATES 503 20.7 SPINORS AS QUBITS 504
21 FINITE ROTATIONS AND TENSOR OPERATORS 509 21.1 MATRICES OF FINITE
ROTATIONS 509 21.2 SPHERICAL FUNCTIONS AS MATRIX ELEMENTS OF FINITE
ROTATIONS 511 21.3 ADDITION THEOREM* 514 21.4 TRANSFORMATION OF
OPERATORS 516 21.5 INTRODUCTION TO SELECTION RULES 528 21.6
ELECTROMAGNETIC MULTIPOLES 519
22 ANGULAR MOMENTUM COUPLING 523 22.1 TWO SUBSYSTEMS 523 22.2
DECOMPOSITION OF REDUCIBLE REPRESENTATIONS 525 22.3 TWO PARTICLES OF
SPIN 1/2 528 22.4 TENSOR OPERATORS AND SELECTION RULES REVISITED 532
22.5 APPLYING TO ELECTROMAGNETIC MULTIPOLES 533 22.6 VECTOR COUPLING OF
ANGULAR MOMENTA 534 22.7 WIGNER-ECKART THEOREM 538 22.8 VECTOR MODEL 539
22.9 ELECTRIC DIPOLE MOMENT AND ANAPOLE MOMENT 542 22.10 CLEBSCH-GORDAN
SERIES* 543
23 FINE AND HYPERFINE STRUCTURE 545 23.1 SPIN-ORBIT COUPLING 545 23.2
SPIN-ORBIT SPLITTING 547 23.3 HYDROGEN FINE STRUCTURE 550 23.4 FINE
STRUCTURE IN COMPLEX ATOMS 553 23.5 MAGNETIC MOMENT WITH SPIN-ORBIT
COUPLING 555 23.6 MAGNETIC HYPERFINE STRUCTURE 558 23.7 EXAMPLE: ONE
VALENCE ELECTRON 560 23.8 QUADRUPOLE HYPERFINE STRUCTURE 562
24 ATOM IN A STATIC FIELD 567 24.1 POLARIZABILITY IN A STATIC ELECTRIC
FIELD 567
IMAGE 7
CONTENTS I XI
24.2 STARK EFFECT 569
24.3 POLARIZABILITY OF THE HYDROGEN ATOM 570 24.4 STARK EFFECT IN THE
HYDROGEN ATOM 572 24.5 NON-UNIFORM ELECTRIC FIELD AND ADDITIONAL
COMMENTS 573 24.6 CLASSICAL ZEEMAN EFFECT 574 24.7 A QUANTUM SYSTEM IN A
MAGNETIC FIELD 575 24.8 NORMAL QUANTUM ZEEMAN EFFECT 576 24.9 ANOMALOUS
QUANTUM ZEEMAN EFFECT 578 24.10 STRONGER MAGNETIC FIELD 579
24.11 DIAMAGNETISM 582
24.12 TOWARDS REALLY STRONG MAGNETIC FIELDS 583
REFERENCES 587
FURTHER READINGS 591
INDEX 597 |
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| title | Quantum Physics |
| title_auth | Quantum Physics |
| title_exact_search | Quantum Physics |
| title_full | Quantum Physics Vladimir Zelevinsky |
| title_fullStr | Quantum Physics Vladimir Zelevinsky |
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| title_short | Quantum Physics |
| title_sort | quantum physics |
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