Quantum physics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Heidelberg[u.a.]
Springer
2013
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 725 - 729 |
| Physical Description: | XVI, 741 S. Ill., graph. Darst. 25 cm |
| ISBN: | 9783642345623 364234562X 9783642345630 |
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Record in the Search Index
| _version_ | 1806325511986610176 |
|---|---|
| adam_text |
PART I FROM THE UNCERTAINTY RELATION TO MANY-BODY SYSTEMS
1 QUANTUM MECHANICS OF POINT PARTICLES 3
1.1 LIMITATIONS OF CLASSICAL PHYSICS 4
1.2 HEISENBERG'S UNCERTAINTY RELATION FOR POSITION
AND MOMENTUM 17
1.2.1 UNCERTAINTIES OF OBSERVABLES 18
1.2.2 QUANTUM MECHANICAL UNCERTAINTIES OF CANONICALLY
CONJUGATE VARIABLES 21
1.2.3 EXAMPLES FOR HEISENBERG'S UNCERTAINTY RELATION 24
1.3 THE PARTICLE-WAVE DUALISM 26
1.3.1 THE WAVE FUNCTION AND ITS INTERPRETATION 28
1.3.2 A FIRST LINK TO CLASSICAL MECHANICS 31
1.3.3 GAUSSIAN WAVE PACKET 32
1.3.4 ELECTRON IN EXTERNAL ELECTROMAGNETIC FIELDS 35
1.4 SCHRODINGER EQUATION AND BORN'S INTERPRETATION
OF THE WAVE FUNCTION 39
1.5 EXPECTATION VALUES AND OBSERVABLES 44
1.5.1 OBSERVABLES AS SELF-ADJOINT OPERATORS ON L
2
(R
3
) 46
1.5.2 EHRENFEST'S THEOREM 49
1.6 A DISCRETE SPECTRUM: HARMONIC OSCILLATOR IN ONE DIMENSION. . . 51
1.7 ORTHOGONAL POLYNOMIALS IN ONE REAL VARIABLE 63
1.8 OBSERVABLES AND EXPECTATION VALUES 70
1.8.1 OBSERVABLES WITH NONDEGENERATE SPECTRUM 70
1.8.2 AN EXAMPLE: COHERENT STATES 75
1.8.3 OBSERVABLES WITH DEGENERATE, DISCRETE SPECTRUM 78
1.8.4 OBSERVABLES WITH PURELY CONTINUOUS SPECTRUM 83
1.9 CENTRAL FORCES AND THE SCHRODINGER EQUATION 88
1.9.1 THE ORBITAL ANGULAR MOMENTUM: EIGENVALUES
AND EIGENFUNCTIONS 88
1.9.2 RADIAL MOMENTUM AND KINETIC ENERGY 98
1.9.3 FORCE FREE MOTION WITH SHARP ANGULAR MOMENTUM . 100
HTTP://D-NB.INFO/1026665582
CONTENTS
1.9.4 THE SPHERICAL OSCILLATOR 107
1.9.5 MIXED SPECTRUM: THE HYDROGEN ATOM 113
2 SCATTERING OF PARTICLES BY POTENTIALS 123
2.1 MACROSCOPIC AND MICROSCOPIC SCALES 123
2.2 SCATTERING ON A CENTRAL POTENTIAL 125
2.3 PARTIAL WAVE ANALYSIS 129
2.3.1 HOW TO CALCULATE SCATTERING PHASES 134
2.3.2 POTENTIALS WITH INFINITE RANGE: COULOMB POTENTIAL 138
2.4 BORN SERIES AND BORN APPROXIMATION 141
2.4.1 FIRST BORN APPROXIMATION 143
2.4.2 FORM FACTORS IN ELASTIC SCATTERING 145
2.5 * ANALYTICAL PROPERTIES OF PARTIAL WAVE AMPLITUDES 149
2.5.1 JOST FUNCTIONS 150
2.5.2 DYNAMIC AND KINEMATIC CUTS 151
2.5.3 PARTIAL WAVE AMPLITUDES AS ANALYTIC FUNCTIONS 154
2.5.4 RESONANCES 155
2.5.5 SCATTERING LENGTH AND EFFECTIVE RANGE 157
2.6 INELASTIC SCATTERING AND PARTIAL WAVE ANALYSIS 160
3 THE PRINCIPLES OF QUANTUM THEORY 165
3.1 REPRESENTATION THEORY 165
3.1.1 DIRAC'S BRACKET NOTATION 168
3.1.2 TRANSFORMATIONS RELATING DIFFERENT REPRESENTATIONS . 171
3.2 THE CONCEPT OF HILBERT SPACE 174
3.2.1 DEFINITION OF HILBERT SPACES 175
3.2.2 SUBSPACES OF HILBERT SPACES 180
3.2.3 DUAL SPACE OF A HILBERT SPACE AND DIRAC'S NOTATION . 182
3.3 LINEAR OPERATORS ON HILBERT SPACES 183
3.3.1 SELF-ADJOINT OPERATORS 184
3.3.2 PROJECTION OPERATORS 188
3.3.3 SPECTRAL THEORY OF OBSERVABLES 189
3.3.4 UNITARY OPERATORS 193
3.3.5 TIME EVOLUTION OF QUANTUM SYSTEMS 195
3.4 QUANTUM STATES 196
3.4.1 PREPARATION OF STATES 197
3.4.2 STATISTICAL OPERATOR AND DENSITY MATRIX 200
3.4.3 DEPENDENCE OF A STATE ON ITS HISTORY 202
3.4.4 EXAMPLES FOR PREPARATION OF STATES 205
3.5 A FIRST SUMMARY 206
3.6 SCHRODINGER AND HEISENBERG PICTURES 208
CONTENTS XIII
4 SPACE-TIME SYMMETRIES IN QUANTUM PHYSICS 211
4.1 THE ROTATION GROUP (PART 1) 211
4.1.1 GENERATORS OF THE ROTATION GROUP 212
4.1.2 REPRESENTATIONS OF THE ROTATION GROUP 214
4.1.3 THE ROTATION MATRICES 220
4.1.4 EXAMPLES AND SOME FORMULAE FOR D-MATRICES 223
4.1.5 SPIN AND MAGNETIC MOMENT OF PARTICLES WITH
J =
1/2 . . . 224
4.1.6 CLEBSCH-GORDAN SERIES AND COUPLING
OF ANGULAR MOMENTA 227
4.1.7 SPIN AND ORBITAL WAVE FUNCTIONS 230
4.1.8 PURE AND MIXED STATES FOR SPIN 1/2 231
4.2 SPACE REFLECTION AND TIME REVERSAL IN QUANTUM MECHANICS . . . 233
4.2.1 SPACE REFLECTION AND PARITY 233
4.2.2 REVERSAL OF MOTION AND OF TIME 236
4.2.3 CONCLUDING REMARKS ON T AND
N
239
4.3 SYMMETRY AND ANTISYMMETRY OF IDENTICAL PARTICLES 242
4.3.1 TWO DISTINCT PARTICLES IN INTERACTION 242
4.3.2 IDENTICAL PARTICLES WITH THE EXAMPLE
N
= 2 245
4.3.3 EXTENSION TO
N
IDENTICAL PARTICLES 249
4.3.4 CONNECTION BETWEEN SPIN AND STATISTICS 250
5 APPLICATIONS OF QUANTUM MECHANICS 255
5.1 CORRELATED STATES AND QUANTUM INFORMATION 255
5.1.1 NONLOCALITIES, ENTANGLEMENT, AND CORRELATIONS 256
5.1.2 ENTANGLEMENT, MORE GENERAL CONSIDERATIONS 262
5.1.3 CLASSICAL AND QUANTUM BITS 265
5.2 STATIONARY PERTURBATION THEORY 269
5.2.1 PERTURBATION OF A NONDEGENERATE ENERGY SPECTRUM 269
5.2.2 PERTURBATION OF A SPECTRUM WITH DEGENERACY 273
5.2.3 AN EXAMPLE: STARK EFFECT 275
5.2.4 TWO MORE EXAMPLES: TWO-STATE SYSTEM,
ZEEMAN-EFFECT OF HYPERFINE STRUCTURE IN MUONIUM 277
5.3 TIME DEPENDENT PERTURBATION THEORY AND TRANSITION
PROBABILITIES 285
5.3.1 PERTURBATIVE EXPANSION OF TIME DEPENDENT
WAVE FUNCTION 287
5.3.2 FIRST ORDER AND FERMI'S GOLDEN RULE 288
5.4 STATIONARY STATES OF N IDENTICAL FERMIONS 291
5.4.1 SELF CONSISTENCY AND HARTREE'S METHOD 292
5.4.2 THE METHOD OF SECOND QUANTIZATION 293
5.4.3 THE HARTREE-FOCK EQUATIONS 296
5.4.4 HARTREE-FOCK EQUATIONS AND RESIDUAL INTERACTIONS 299
XIV
CONTENTS
5.4.5 PARTICLE AND HOLE STATES, NORMAL PRODUCT
AND WICK'S THEOREM 301
5.4.6 APPLICATION TO THE HARTREE-FOCK GROUND STATE 304
PART II FROM SYMMETRIES IN QUANTUM PHYSICS
TO ELECTROWEAK INTERACTIONS
6 SYMMETRIES AND SYMMETRY GROUPS IN QUANTUM PHYSICS 311
6.1 ACTION OF SYMMETRIES AND WIGNER'S THEOREM 312
6.1.1 COHERENT SUBSPACES OF HILBERT SPACE 313
6.1.2 WIGNER'S THEOREM 316
6.2 THE ROTATION GROUP (PART 2) 319
6.2.1 RELATIONSHIP BETWEEN
SU(2)
AND 50(3) 320
6.2.2 THE IRREDUCIBLE UNITARY REPRESENTATIONS OF
SU(2)
323
6.2.3 ADDITION OF ANGULAR MOMENTA
AND CLEBSCH-GORDAN COEFFICIENTS 335
6.2.4 CALCULATING CLEBSCH-GORDAN COEFFICIENTS;
THE 3Y-SYMBOLS 339
6.2.5 TENSOR OPERATORS AND WIGNER-ECKART THEOREM 343
6.2.6 *INTERTWINER, 6J- AND 9Y-SYMBOLS 349
6.2.7 REDUCED MATRIX ELEMENTS IN COUPLED STATES 356
6.2.8 REMARKS ON COMPACT LIE GROUPS
AND INTERNAL SYMMETRIES 359
6.3 LORENTZ- AND POINCARE GROUPS 364
6.3.1 THE GENERATORS OF THE LORENTZ AND POINCARE GROUPS . 365
6.3.2 ENERGY-MOMENTUM, MASS AND SPIN 370
6.3.3 PHYSICAL REPRESENTATIONS OF THE POINCARE GROUP 372
6.3.4 MASSIVE SINGLE-PARTICLE STATES AND POINCARE GROUP 377
7 QUANTIZED FIELDS AND THEIR INTERPRETATION 383
7.1 THE KLEIN-GORDON FIELD 384
7.1.1 THE COVARIANT NORMALIZATION 388
7.1.2 A COMMENT ON PHYSICAL UNITS 389
7.1.3 SOLUTIONS OF THE KLEIN-GORDON EQUATION
FOR FIXED FOUR-MOMENTUM 392
7.1.4 QUANTIZATION OF THE REAL KLEIN-GORDON FIELD 395
7.1.5 NORMAL MODES, CREATION AND ANNIHILATION OPERATORS . . . 397
7.1.6 COMMUTATOR FOR DIFFERENT TIMES, PROPAGATOR 404
7.2 THE COMPLEX KLEIN-GORDON FIELD 409
7.3 THE QUANTIZED MAXWELL FIELD 415
7.3.1 MAXWELL'S THEORY IN THE LAGRANGE FORMALISM 416
7.3.2 CANONICAL MOMENTA, HAMILTON- AND MOMENTUM
DENSITIES 419
CONTENTS XV
7.3.3 LORENZ-AND TRANSVERSAL GAUGES 420
7.3.4 QUANTIZATION OF THE MAXWELL FIELD 423
7.3.5 ENERGY, MOMENTUM, AND SPIN OF PHOTONS 426
7.3.6 HELICITY AND ORBITAL ANGULAR MOMENTUM OF PHOTONS. . . . 427
7.4 INTERACTION OF THE QUANTUM MAXWELL FIELD WITH MATTER 431
7.4.1 MANY-PHOTON STATES AND MATRIX ELEMENTS 432
7.4.2 ABSORPTION AND EMISSION OF SINGLE PHOTONS 433
7.4.3 RAYLEIGH- AND THOMSON SCATTERING 439
7.5 COVARIANT QUANTIZATION OF THE MAXWELL FIELD 445
7.5.1 GAUGE FIXING AND QUANTIZATION 446
7.5.2 NORMAL MODES AND ONE-PHOTON STATES 448
7.5.3 LORENZ CONDITION, ENERGY AND MOMENTUM
OF THE RADIATION FIELD 450
7.6 *THE STATE SPACE OF QUANTUM ELECTRODYNAMICS 452
7.6.1 *FIELD OPERATORS AND MAXWELL'S EQUATIONS 453
7.6.2 *THE METHOD OF GUPTA AND BLEULER 456
7.7 PATH INTEGRALS AND QUANTIZATION 460
7.7.1 THE ACTION IN CLASSICAL MECHANICS 460
7.7.2 THE ACTION IN QUANTUM MECHANICS 462
7.7.3 CLASSICAL AND QUANTUM PATHS 465
7.8 PATH INTEGRAL FOR FIELD THEORIES 466
7.8.1 THE FUNCTIONAL DERIVATIVE 467
7.8.2 FUNCTIONAL POWER SERIES AND TAYLOR SERIES 468
7.8.3 GENERATING FUNCTIONAL 469
7.8.4 AN EXAMPLE: PROPAGATOR OF THE SCALAR FIELD 471
7.8.5 COMPLEX SCALAR FIELD AND PATH INTEGRALS 473
8 SCATTERING MATRIX AND OBSERVABLES IN SCATTERING AND DECAYS . 477
8.1 NONRELATIVISTIC SCATTERING THEORY IN AN OPERATOR FORMALISM. . . .
477
8.1.1 THE LIPPMANN-SCHWINGER EQUATION 477
8.1.2 /"-MATRIX AND SCATTERING AMPLITUDE 481
8.2 COVARIANT SCATTERING THEORY 482
8.2.1 ASSUMPTIONS AND CONVENTIONS 482
8.2.2 S-MATRIX AND OPTICAL THEOREM 483
8.2.3 CROSS SECTIONS FOR TWO PARTICLES 489
8.2.4 DECAY WIDTHS OF UNSTABLE PARTICLES 495
8.3 COMMENT ON THE SCATTERING OF WAVE PACKETS 500
9 PARTICLES WITH SPIN 1/2 AND THE DIRAC EQUATION 501
9.1 RELATIONSHIP BETWEEN SL(2,C) DTX L+ 502
9.1.1 REPRESENTATIONS WITH SPIN 1/2 505
9.1.2 *DIRAC EQUATION IN MOMENTUM SPACE 507
9.1.3 SOLUTIONS OF THE DIRAC EQUATION IN MOMENTUM SPACE . 515
9.1.4 DIRAC EQUATION IN SPACETIME AND LAGRANGE DENSITY . 519
XVI CONTENTS
9.2 QUANTIZATION OF THE DIRAC FIELD 523
9.2.1 QUANTIZATION OF MAJORANA FIELDS 524
9.2.2 QUANTIZATION OF DIRAC FIELDS 527
9.2.3 ELECTRIC CHARGE, ENERGY, AND MOMENTUM 531
9.3 DIRAC FIELDS AND INTERACTIONS 533
9.3.1 SPIN AND SPIN DENSITY MATRIX 533
9.3.2 THE FERMION-ANTIFERMION PROPAGATOR 539
9.3.3 TRACES OF PRODUCTS OF Y-MATRICES 541
9.3.4 CHIRAL STATES AND THEIR COUPLINGS TO SPIN-1 PARTICLES . . . 546
9.4 WHEN IS THE DIRAC EQUATION A ONE-PARTICLE THEORY? 555
9.4.1 SEPARATION OF THE DIRAC EQUATION IN POLAR COORDINATES. . . 556
9.4.2 HYDROGEN-LIKE ATOMS FROM THE DIRAC EQUATION 560
9.5 PATH INTEGRALS WITH FERMIONIC FIELDS 568
10 ELEMENTS OF QUANTUM ELECTRODYNAMICS AND WEAK INTERACTIONS . . . 573
10.1 S-MATRIX AND PERTURBATION SERIES 573
10.1.1 TOOLS OF QUANTUM ELECTRODYNAMICS WITH LEPTONS 577
10.1.2 FEYNMAN RULES FOR QUANTUM ELECTRODYNAMICS
WITH CHARGED LEPTONS 580
10.1.3 SOME PROCESSES IN TREE APPROXIMATION 584
10.2 RADIATIVE CORRECTIONS, REGULARIZATION, AND RENORMALIZATION . 601
10.2.1 SELF-ENERGY OF ELECTRONS TO ORDER
O
(E
2
)
601
10.2.2 RENORMALIZATION OF THE FERMION MASS 606
10.2.3 SCATTERING ON AN EXTERNAL POTENTIAL 609
10.2.4 VERTEX CORRECTION AND ANOMALOUS MAGNETIC MOMENT. . . 617
10.2.5 VACUUM POLARIZATION 624
10.3 EPILOGUE: QUANTUM ELECTRODYNAMICS IN THE FRAMEWORK
OF ELECTROWEAK INTERACTIONS 639
10.3.1 WEAK INTERACTIONS WITH CHARGED CURRENTS 640
10.3.2 PURELY LEPTONIC PROCESSES AND MUON DECAY 643
10.3.3 TWO SIMPLE SEMI-LEPTONIC PROCESSES 649
APPENDIX 653
HISTORICAL NOTES 681
EXERCISES, HINTS, AND SELECTED SOLUTIONS 691
REFERENCES 725
INDEX 731
ABOUT THE AUTHOR 741 |
| any_adam_object | 1 |
| author | Scheck, Florian 1936-2024 |
| author_GND | (DE-588)121611493 |
| author_facet | Scheck, Florian 1936-2024 |
| author_role | aut |
| author_sort | Scheck, Florian 1936-2024 |
| author_variant | f s fs |
| building | Verbundindex |
| bvnumber | BV041199931 |
| classification_rvk | UK 1000 |
| ctrlnum | (OCoLC)849717853 (DE-599)DNB1026665582 |
| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 2. ed. |
| format | Book |
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| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV041199931 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T00:50:46Z |
| institution | BVB |
| isbn | 9783642345623 364234562X 9783642345630 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026174830 |
| oclc_num | 849717853 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-20 |
| owner_facet | DE-19 DE-BY-UBM DE-20 |
| physical | XVI, 741 S. Ill., graph. Darst. 25 cm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| spelling | Scheck, Florian 1936-2024 Verfasser (DE-588)121611493 aut Quantum physics Florian Scheck 2. ed. Heidelberg[u.a.] Springer 2013 XVI, 741 S. Ill., graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 725 - 729 Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantenphysik (DE-588)4266670-3 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Quantenphysik (DE-588)4266670-3 s DE-604 Quantenmechanik (DE-588)4047989-4 s Quantenfeldtheorie (DE-588)4047984-5 s Erscheint auch als Online-Ausgabe Quantum Physics B:DE-101 application/pdf http://d-nb.info/1026665582/04 Inhaltsverzeichnis X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4157692&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026174830&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Scheck, Florian 1936-2024 Quantum physics Quantenfeldtheorie (DE-588)4047984-5 gnd Quantenphysik (DE-588)4266670-3 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4266670-3 (DE-588)4047989-4 (DE-588)4123623-3 |
| title | Quantum physics |
| title_auth | Quantum physics |
| title_exact_search | Quantum physics |
| title_full | Quantum physics Florian Scheck |
| title_fullStr | Quantum physics Florian Scheck |
| title_full_unstemmed | Quantum physics Florian Scheck |
| title_short | Quantum physics |
| title_sort | quantum physics |
| topic | Quantenfeldtheorie (DE-588)4047984-5 gnd Quantenphysik (DE-588)4266670-3 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantenfeldtheorie Quantenphysik Quantenmechanik Lehrbuch |
| url | http://d-nb.info/1026665582/04 http://deposit.dnb.de/cgi-bin/dokserv?id=4157692&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026174830&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT scheckflorian quantumphysics |
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