Symmetries in quantum physics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
San Diego [u.a.]
Acad. Pr.
1996
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 333 S. graph. Darst. |
| ISBN: | 012248455X 0122484614 |
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Record in the Search Index
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| adam_text | SYMMETRIES IN QUANTUM PHYSICS U. FANO DEPARTMENT OF PHYSICS AND JAMES
FRANCK INSTITUTE UNIVERSITY OF CHICAGO CHICAGO, ILLINOIS A. R. P. RAU
DEPARTMENT OF PHYSICS AND ASTRONOMY LOUISIANA STATE UNIVERSITY BATON
ROUGE, LOUISIANA ACADEMIC PRESS SAN DIEGO NEW YORK BOSTON LONDON SYDNEY
TOKYO TORONTO CONTENTS PREFACE XIII 1 INTRODUCTION 1 TRANSFORMATION
THEORIES: KLEIN S AND DIRAC S 3 1.1 SYMMETRY AND THE SELECTION OF
VARIABLES 5 1.1.1 EXAMPLES OF TENSORIAL EQUATIONS 5 1.2 ALGEBRAIC
ELEMENTS 11 1.2.1 VECTORS, TENSORS, AND RELATED QUANTITIES 11 1.2.2
ADDITION AND DIRECT PRODUCT OF TENSORIAL SETS . . . . 14 1.2.3 LINEAR
TRANSFORMATION 14 1.3 REDUCTION PROCEDURE AND IRREDUCIBLE TENSORIAL SETS
17 1.3.1 AN ANALYTICAL EXAMPLE: REDUCTION OF TENSORS . . . . 18 1.4
FURTHER ASPECTS OF REDUCTION 20 1.4.1 REDUCTION PROCEDURES 21 1.4.2
LABELING OF SET ELEMENTS 22 1.4.3 BLOCK DIAGONALIZATION OF THE REDUCTION
23 1.4.4 PHASE NORMALIZATION 23 1.4.5 GROUP THEORY 24 1.4.6 REDUCTION AS
AN EXPANSION INTO EIGENFUNCTIONS ... 25 1.5 STRUCTURE OF THE BOOK 26
1.5.1 ALTERNATIVE SETS OF COMMUTING INVARIANT OPERATORS 27 1.6
QUATERNIONS 28 PROBLEMS 29 V VI PART A STATE REPRESENTATIVES AND
R-TRANSFORMATIONS: THEIR CONSTRUCTION AND PROPERTIES 2 INFINITESIMAL
ROTATIONS AND ANGULAR MOMENTUM 33 2.1 BASIC RELATIONS 34 2.2 ANALYTICAL
EXAMPLE: INFINITESIMAL TRANSFORMATION OF CARTESIAN COORDINATES . 38 2.3
THE ANGULAR MOMENTUM MATRICES OF QUANTUM MECHANICS 41 2.3.1 PHASE
NORMALIZATION 43 2.3.2 DEFINITION OF A STANDARD BASE 44 2.4 THE
FUNDAMENTAL REPRESENTATION 45 2.4.1 SIGNIFICANCE OF HALF-INTEGER J 47
PROBLEMS 49 3 FRAME REVERSAL AND COMPLEX CONJUGATION 51 3.1 ANALYTICAL
REPRESENTATION AND IMPLICATIONS OF FRAME REVERSAL 54 3.1.1 EXPLICIT FORM
OF THE MATRIX U 58 3.1.2 PROPERTIES OF THE MATRIX U 59 3.2
CONTRAGREDIENCE AND THE CONSTRUCTION OF INVARIANTS 62 3.2.1
CONTRAGREDIENT TENSORIAL SETS 64 3.2.2 INVARIANT PRODUCTS 64 3.2.3
NOTATION 67 3.3 CARTESIAN BASE FOR INTEGER J 1 68 3.3.1
CARTESIAN-TO-STANDARD TRANSFORMATION 70 3.3.2 PHASE NORMALIZATION OF
SPHERICAL HARMONICS 72 PROBLEMS 74 4 STANDARD R-TRANSFORMATION MATRICES
AND THEIR APPLICATIONS 75 4.1 EXPLICIT FORM AND PROPERTIES 76 4.1.1
SPINOR METHOD 78 VLL 4.1.2 ALGEBRAIC APPROACH 80 4.1.3 FIRST ORDER
DIFFERENTIAL SYSTEM 81 4.1.4 SECOND ORDER DIFFERENTIAL EQUATION 82 4.1.5
SYMMETRIES OF THE STANDARD R-TRANSFORMATIONS . ... 82 4.1.6 INTEGRALS 83
4.1.7 R- TRANSFORMATIONS IN THE CARTESIAN FRAME 85 4.2 MACROSCOPIC
APPLICATIONS 85 4.3 APPLICATIONS TO QUANTUM PHYSICS 88 4.3.1 PARTICLE
TRANSMISSION THROUGH A STERN-GERLACH MAGNET 88 4.3.2 ANGULAR
DISTRIBUTION OF A PARTICLE IN ORBITAL MOTION 89 4.3.3 ROTATIONAL
EIGENFUNCTIONS AND EIGENVALUES FOR SYMMETRIC-TOP POLYATOMIC MOLECULES
AND HETERONUCLEAR DIATOMICS 90 4.3.4 SPINOR AND VECTOR HARMONICS 92 4.4
COORDINATE INVERSION AND PARITY EIGENFUNCTIONS 93 PROBLEMS 97 5
REDUCTION OF DIRECT PRODUCTS (ADDITION OF ANGULAR MOMENTA) 99 5.1
STRUCTURE AND PROPERTIES OF THE REDUCING MATRIX 100 5.1.1 SPINOR
APPROACH 102 5.1.2 NORMALIZATION 104 5.1.3 RECURRENCE RELATIONS 107
5.1.4 SYMMETRIES 107 5.1.5 REDUCTION IN THE CARTESIAN FRAME 109 5.2
REDUCTION OF R-TRANSFORMATION PRODUCTS 110 5.3 IRREDUCIBLE PRODUCT SETS
112 5.3.1 SPECIAL CASES 112 5.3.2 SYMMETRY 113 5.3.3 PRODUCTS OF
CONTRAGREDIENT SETS 113 5.3.4 WAVE-MECHANICAL EXAMPLES 114 5.3.5
MULTIPLE PRODUCTS 115 5.3.6 COUPLING DIAGRAMS 116 5.4 SYMMETRIZATION OF
WIGNER COEFFICIENTS: INVARIANT TRIPLE PRODUCT AND 3-J COEFFICIENTS 119
PROBLEMS . 123 VLLL PART * TENSORIAL ASPECTS OF QUANTUM PHYSICS 6
TENSORIAL SETS OF QUANTUM OPERATORS 127 6.1 THE LIOUVILLE REPRESENTATION
OF QUANTUM MECHANICS . . . . 128 6.2 QUANTUM MECHANICS OF PARTICLES WITH
SPIN | 130 6.2.1 BASE SETS OF MATRICES AND OPERATORS 132 6.3 TWO-LEVEL
SYSTEMS 135 6.3.1 ATOM IN A RADIATION FIELD 136 6.3.2 LIGHT POLARIZATION
AND STOKES PARAMETERS 137 6.3.3 FURTHER APPLICATIONS OF TWO-LEVEL
SYSTEMS: OCCUPATION, CREATION, AND ANNIHILATION OPERATORS . . 138 6.4
PARTICLES WITH SPIN J |: WIGNER-ECKART THEOREM 140 6.4.1 DENSITY MATRIX
140 6.4.2 MULTIPOLE EXPANSION OF OPERATORS G 143 6.4.3 PHYSICAL
IMPLICATIONS OF THE TRIANGULAR RELATION * 2J 145 6.5 SYSTEMS WITH 2J +
L LEVELS 146 6.6 TRANSFER OF ANGULAR MOMENTUM 148 6.7 CALCULATION OF
MATRIX ELEMENTS 150 PROBLEMS 154 7 RECOUPLING TRANSFORMATIONS: 6-J AND
9-J COEFFICIENTS 157 7.1 TRANSFORMATION MATRICES AND THEIR ANALYSIS 160
7.1.1 DIAGRAMS 161 7.1.2 GROUP PROPERTIES 162 7.1.3 FACTORIZATION OF
TRANSFORMATIONS 163 7.2 SYMMETRIZED RECOUPLING: 6-J AND 9-J COEFFICIENTS
168 7.2.1 6-J COEFFICIENTS 170 7.2.2 9-J COEFFICIENTS 173 7.2.3
ALTERNATIVE PERSPECTIVES 175 7.3 PRODUCTS OF OPERATORS 176 7.3.1 UNIT
OPERATORS 176 7.3.2 GENERAL OPERATOR 179 7.3.3 COMMUTATORS 180 7.3.4
SCHROEDINGER EQUATION FOR A (2J + L)-LEVEL SYSTEM ... 181 7.4 COMBINING
OPERATORS OF DIFFERENT SYSTEMS 183 IX 7.5 ILLUSTRATIONS 186 7.5.1
INTERACTION MATRIX ELEMENTS 187 7.5.2 PROJECTION OF OPERATORS 189 7.5.3
CORRELATIONS 191 PROBLEMS 195 8 PARTIALLY FILLED SHELLS OF ATOMS OR
NUCLEI 199 8.1 QUALITATIVE DISCUSSION 200 8.1.1 TWO-PARTICLE STATES 202
8.1.2 STATES OF THREE OR MORE EQUIVALENT PARTICLES 202 8.1.3 QUANTUM
NUMBERS FOR MANY-PARTICLE STATES 204 8.2 SHELL-WIDE TREATMENT 208 8.2.1
TRIPLE TENSORS AND THEIR MATRICES 210 8.2.2 COEFFICIENTS OF FRACTIONAL
PARENTAGE 213 8.3 ALGEBRA OF TRIPLE TENSORS AND ITS APPLICATIONS 214
8.3.1 INTERPRETATION OF *(**.**) 215 8.3.2 QUASI-SPIN AND SENIORITY 217
8.3.3 QUASIPARTICLES FOR THE / SHELL 218 8.3.4 DETERMINATION OF
FRACTIONAL PARENTAGE 220 8.3.5 OPERATOR MATRICES 224 PART * SYMMETRIES
OF HIGHER DIMENSIONS 9 DISCRETE TRANSFORMATIONS OF COORDINATES 229 9.1
POINT SYMMETRY OPERATIONS AND THEIR GROUPS 230 9.2 CHARACTERS OF GROUP
REPRESENTATIONS AND THEIR APPLICATIONS 235 9.2.1 ABELIAN GROUPS 235
9.2.2 NON-ABELIAN GROUPS 237 9.2.3 CHARACTERS OF THE ROTATION GROUP
50(3) 239 9.2.4 REDUCTION OF REPRESENTATIONS 240 9.2.5 REDUCTION OF SET
PRODUCTS 242 9.3 SYMMETRIES OF MOLECULES AND CRYSTALS 243 X 9.3.1
SYMMETRY COMBINATIONS 244 9.3.2 VIBRATIONAL MOTIONS 245 9.3.3 MOLECULAR
ROTATIONS 245 9.3.4 STABILITY ANALYSIS OF NUCLEAR POSITIONS 246 PROBLEMS
250 10 ROTATION GROUPS IN HIGHER DIMENSIONS: MULTIPARTICLE PROBLEMS 251
10.1 FOUR-DIMENSIONAL ROTATIONS: THE COULOMB-KEPLER PROBLEM 252 10.1.1
SPHERICAL AND PARABOLIC REPRESENTATIONS 253 10.1.2 ROTATIONS IN FOUR
DIMENSIONS 255 10.1.3 HYDROGEN ATOM IN MOMENTUM SPACE 258 10.1.4
ALTERNATIVE SUBGROUPS OF 50(4): THE HYDROGEN ATOM IN EXTERNAL FIELDS 259
10.1.5 CLEBSCH-GORDAN COEFFICIENTS FOR PRODUCTS OF 50(4) . 261 10.2
ORTHOGONAL GROUPS IN HIGHER DIMENSIONS 263 10.2.1 HYPERSPHERE IN D
DIMENSIONS 264 10.2.2 HYPERSPHERICAL COORDINATES FOR MULTIPARTICLE
SYSTEMS 267 10.2.3 TRANSFORMATION BETWEEN ALTERNATIVE SCHEMES 271 10.3
FURTHER DEVELOPMENTS 272 10.3.1 INVARIANCE AND NONINVARIANCE GROUPS 272
10.3.2 DYNAMICAL SYMMETRIES FOR ATOMS AND NUCLEI . . . 274 10.3.3
ADJOINING AN EXTRA DEGREE OF FREEDOM 276 10.3.4 ALTERNATIVE REDUCTION
SCHEMES FOR MULTIPARTICLE SYSTEMS 277 11 LORENTZ TRANSFORMATIONS AND THE
LORENTZ AND POINCARE GROUPS 279 11.1 LORENTZ TRANSFORMATIONS 281 11.2
GENERATORS AND REPRESENTATIONS OF THE LORENTZ GROUP . . . 283 11.2.1
FOUR-VECTORS AND THE LORENTZ METRIC 284 11.2.2 GENERATORS OF THE PROPER
LORENTZ GROUP 285 11.2.3 LORENTZ TRANSFORMATIONS TO R-TRANSFORMATIONS .
. . . 287 11.2.4 SPINOR REPRESENTATIONS 289 11.2.5 NEUTRINO AND ELECTRON
SPINOR STATES 291 11.2.6 ELECTROMAGNETISM AND ITS QUANTUM 294 11.3 THE
INHOMOGENEOUS LORENTZ (POINCARE) GROUP 295 11.3.1 GENERATORS AND
COMMUTATION RELATIONSHIPS 296 11.4 FIELD REPRESENTATIONS 297 11.4.1
MASSIVE SYSTEMS 298 11.4.2 REPRESENTATIONS OF MASSLESS ENTITIES 299 12
SYMMETRIES OF THE SCATTERING CONTINUUM 301 12.1 SYMMETRIES OF RADIAL
EIGENFUNCTIONS 302 12.2 THE FULL NONINVARIANCE GROUP OF HYDROGEN 305
12.2.1 ALTERNATIVE DECOMPOSITIONS OF THE NONINVARIANCE GROUP 308 12.3
DYNAMICS AND SYMMETRY TRANSFORMATIONS 310 BIBLIOGRAPHY 313 INDEX 317
|
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| indexdate | 2024-07-09T18:01:30Z |
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| publisher | Acad. Pr. |
| record_format | marc |
| spelling | Fano, Ugo Verfasser aut Symmetries in quantum physics U. Fano ; A. R. P. Rau San Diego [u.a.] Acad. Pr. 1996 XIV, 333 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematik Mathematische Physik Quantentheorie Mathematical physics Quantum theory Mathematics Symmetry (Physics) Methodology Quantentheorie (DE-588)4047992-4 gnd rswk-swf Atomstoß (DE-588)4135380-8 gnd rswk-swf Quantenphysik (DE-588)4266670-3 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Atomspektrum (DE-588)4143334-8 gnd rswk-swf Symmetrie (DE-588)4058724-1 gnd rswk-swf Quantentheorie (DE-588)4047992-4 s Symmetrie (DE-588)4058724-1 s DE-604 Mathematische Physik (DE-588)4037952-8 s Quantenphysik (DE-588)4266670-3 s Atomstoß (DE-588)4135380-8 s Atomspektrum (DE-588)4143334-8 s Rau, A. R. P. Verfasser (DE-588)124449468 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007322248&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fano, Ugo Rau, A. R. P. Symmetries in quantum physics Mathematik Mathematische Physik Quantentheorie Mathematical physics Quantum theory Mathematics Symmetry (Physics) Methodology Quantentheorie (DE-588)4047992-4 gnd Atomstoß (DE-588)4135380-8 gnd Quantenphysik (DE-588)4266670-3 gnd Mathematische Physik (DE-588)4037952-8 gnd Atomspektrum (DE-588)4143334-8 gnd Symmetrie (DE-588)4058724-1 gnd |
| subject_GND | (DE-588)4047992-4 (DE-588)4135380-8 (DE-588)4266670-3 (DE-588)4037952-8 (DE-588)4143334-8 (DE-588)4058724-1 |
| title | Symmetries in quantum physics |
| title_auth | Symmetries in quantum physics |
| title_exact_search | Symmetries in quantum physics |
| title_full | Symmetries in quantum physics U. Fano ; A. R. P. Rau |
| title_fullStr | Symmetries in quantum physics U. Fano ; A. R. P. Rau |
| title_full_unstemmed | Symmetries in quantum physics U. Fano ; A. R. P. Rau |
| title_short | Symmetries in quantum physics |
| title_sort | symmetries in quantum physics |
| topic | Mathematik Mathematische Physik Quantentheorie Mathematical physics Quantum theory Mathematics Symmetry (Physics) Methodology Quantentheorie (DE-588)4047992-4 gnd Atomstoß (DE-588)4135380-8 gnd Quantenphysik (DE-588)4266670-3 gnd Mathematische Physik (DE-588)4037952-8 gnd Atomspektrum (DE-588)4143334-8 gnd Symmetrie (DE-588)4058724-1 gnd |
| topic_facet | Mathematik Mathematische Physik Quantentheorie Mathematical physics Quantum theory Mathematics Symmetry (Physics) Methodology Atomstoß Quantenphysik Atomspektrum Symmetrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007322248&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT fanougo symmetriesinquantumphysics AT rauarp symmetriesinquantumphysics |