The Pauli exclusion principle: origin, verifications, and applications
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester
Wiley
2017
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | xii, 238 Seiten Illustrationen |
| ISBN: | 9781118795323 |
Internformat
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| 245 | 1 | 0 | |a The Pauli exclusion principle |b origin, verifications, and applications |c Ilya G. Kaplan (Materials Research Institute, National Autonomous University of Mexico, Mexico) |
| 264 | 1 | |a Chichester |b Wiley |c 2017 | |
| 300 | |a xii, 238 Seiten |b Illustrationen | ||
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| 650 | 7 | |a Quantum theory |2 fast | |
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| 650 | 7 | |a SCIENCE / Physics / General |2 bisacsh | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Pauli exclusion principle | |
| 650 | 4 | |a Quantum theory | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
A
Preface xi
1 Historical Survey 1
1.1 Discovery of the Pauli Exclusion Principle and Early
Developments 1
1.2 Further Developments and Still Existing Problems 11
References 21
2 Construction of Functions with a Definite Permutation Symmetry 25
2.1 Identical Particles in Quantum Mechanics and Indistinguishability
Principle 25
2.2 Construction of Permutation-Symmetric Functions Using the
Young Operators 29
2.3 The Total Wave Functions as a Product of Spatial and
Spin Wave Functions 36
2.3.7 Two-Particle System 36
2.3.2 General Case of N-Particle System 41
References 49
3 Can the Pauli Exclusion Principle Be Proved? 50
3.1 Critical Analysis of the Existing Proofs of the
Pauli Exclusion Principle 50
3.2 Some Contradictions with the Concept of Particle Identity and
their Independence in the Case of the Multidimensional
Permutation Representations 56
References 62
• · «
Vlll
Contents
4 Classification of the Pauli-Allowed States in Atoms and Molecules 64
4.1 Electrons in a Central Field 64
4.1.1 Equivalent Electrons: L—S Coupling 64
4.1.2 Additional Quantum Numbers: The Seniority Number 71
4.1.3 Equivalent Electrons: j—j Coupling 72
4.2 The Connection between Molecular Terms and Nuclear Spin 74
4.2.1 Classification of Molecular Terms and the Total
Nuclear Spin 74
4.2.2 The Determination of the Nuclear Statistical Weights
of Spatial States 79
4.3 Determination of Electronic Molecular Multiplets 82
4.3.1 Valence Bond Method 82
4.3.2 Degenerate Orbitals and One Valence Electron on
Each Atom 87
4.3.3 Several Electrons Specified on One of the Atoms 91
4.3.4 Diatomic Molecule with Identical Atoms 93
4.3.5 General Case I 98
4.3.6 General Case II 100
References 104
5 Parastatistics, Fractional Statistics, and Statistics of
Quasiparticles of Different Kind 106
5.1 Short Account of Parastatistics 106
5.2 Statistics of Quasiparticles in a Periodical Lattice 109
5.2.1 Holes as Collective States 109
5.2.2 Statistics and Some Properties of Holon Gas 111
5.2.3 Statistics of Hole Pairs 111
5.3 Statistics of Cooper’s Pairs 121
5.4 Fractional Statistics 124
5.4.1 Eigenvalues of Angular Momentum in the
Three- and Two-Dimensional Space 124
5.4.2 Anyons and Fractional Statistics 128
References 133
Appendix A: Necessary Basic Concepts and Theorems of
Group Theory 135
A.l Properties of Group Operations 135
A. 1.1 Group Postulates 135
A. 1.2 Examples of Groups 137
A. 1.3 Isomorphism and Homomorphism 138
A. 1.4 Subgroups and Cosets 139
A. 1.5 Conjugate Elements. Classes 140
Contents
ix
A. 2 Representation of Groups 141
A. 2.1 Definition 141
A.2.2 Vector Spaces 142
A, 2.3 Reducibility of Representations 145
A.2.4 Properties of Irreducible Representations 147
A. 2.5 Characters 148
A.2.6 The Decomposition of a Reducible Representation 149
A. 2.7 The Direct Product of Representations 151
A. 2.8 Clebsch—Gordan Coefficients 154
A.2.9 The Regular Representation 156
A. 2Л0 The Construction of Basis Functions for
Irreducible Representation 157
References 160
Appendix B: The Permutation Group 161
B. 1 General Information 161
ВЛЛ Operations with Permutation 161
B. 1.2 Classes 164
B.1.3 Young Diagrams and Irreducible Representations 165
B. 2 The Standard Young-Yamanouchi Orthogonal Representation 167
B.2.1 Young Tableaux 167
B.2.2 Explicit Determination of the Matrices of the
Standard Representation 170
B.2.3 The Conjugate Representation 173
B.2.4 The Construction of an Antisymmetric Function from the
Basis Functions for Two Conjugate Representations 175
B.2.5 Young Operators 176
B. 2.6 The Construction of Basis Functions for the Standard
Representation from a Product of N Orthogonal Functions 178
References 181
Appendix C: The Interconnection between Linear Groups and
Permutation Groups 182
C. l Continuous Groups 182
C. l.I Definition 182
C.l.2 Examples of Linear Groups 185
C.1.3 Infinitesimal Operators 187
C.2 The Three-Dimensional Rotation Group 189
C.2.1 Rotation Operators and Angular Momentum Operators 189
C.2.2 Irreducible Representations 191
C.2.3 Reduction of the Direct Product of Two Irreducible
Representations 194
X
Contents
C.2.4 Reduction of the Direct Product ofk Irreducible
Representations. 3n — j Symbols 197
C.3 Tensor Representations 201
C.3.1 Construction of a Tensor Representation 201
C.3.2 Reduction of a Tensor Representation into
Reducible Components 202
C.3.3 Littlewood s Theorem 207
C.3.4 The Reduction of U2j +1 —» R3 209
C. 4 Tables of the Reduction of the Representations U^J+ x
to the Group R3 214
References 216
Appendix D: Irreducible Tensor Operators 217
D. l Definition 217
D.2 The Wigner-Eckart Theorem 220
References 222
Appendix E: Second Quantization 223
References 227
Index 228
THE PAULI EXCLUSION PRINCIPLE
ORIGIN. VERIFICATIONS. AND APPLICATIONS
ILYA G. KAPLAN
Materials Research Institute, National Autonomous University of Mexico, Mexico
This is the first scientific book devoted to the Pauli exclusion principle, which is
a fundamental principle of quantum mechanics and is permanently applied in
chemistry, physics, and molecular biology. However, while the principle has been
studied for more than 90 years, rigorous theoretical foundations still have not been
established and many unsolved problems remain.
Following a historical survey in Chapter 1, the book discusses the still unresolved
questions around this fundamental principle. For instance, why, according to
the Pauli exclusion principle, are only symmetric and antisymmetric permutation
symmetries for identical particles realized, while the Schrödinger equation is
satisfied by functions with any permutation symmetry? Chapter 3 covers possible
answers to this question. The construction of function with a given permutation
symmetry is described in the previous Chapter 2, while Chapter 4 presents effective
and elegant methods for finding the Pauli-allowed states in atomic, molecular, and
nuclear spectroscopy. Chapter 5 discusses parastatistics and fractional statistics,
demonstrating that the quasiparticles in a periodical lattice, including excitons and
magnons, are obeying modified parafermi statistics.
With detailed appendices, The Pauli Exclusion Principle: Origin, Verifications,
and Applications is intended as a self-sufficient guide for graduate students and
academic researchers in the fields of chemistry, physics, molecular biology, and
applied mathematics. It will be a valuable resource for any reader interested in the
foundations of quantum mechanics and its applications, including areas such as
atomic and molecular spectroscopy, spintronics, theoretical chemistry, and applied
fields of quantum information.
www.wiley.com
Wiley
3| Also available
___I as an e-book
ISBN 978-1-118-79532-3
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| spelling | Kaplan, Ilya G. 1932- Verfasser (DE-588)1128845083 aut The Pauli exclusion principle origin, verifications, and applications Ilya G. Kaplan (Materials Research Institute, National Autonomous University of Mexico, Mexico) Chichester Wiley 2017 xii, 238 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Pauli exclusion principle fast Quantum theory fast SCIENCE / Energy bisacsh SCIENCE / Mechanics / General bisacsh SCIENCE / Physics / General bisacsh Quantentheorie Pauli exclusion principle Quantum theory Pauli-Prinzip (DE-588)4173571-7 gnd rswk-swf Pauli-Prinzip (DE-588)4173571-7 s DE-604 Erscheint auch als 978-1-118-79529-3 Online-Ausgabe, epdf Erscheint auch als 978-1-118-79524-8 Online-Ausgabe, epub Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029589635&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029589635&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Kaplan, Ilya G. 1932- The Pauli exclusion principle origin, verifications, and applications Pauli exclusion principle fast Quantum theory fast SCIENCE / Energy bisacsh SCIENCE / Mechanics / General bisacsh SCIENCE / Physics / General bisacsh Quantentheorie Pauli exclusion principle Quantum theory Pauli-Prinzip (DE-588)4173571-7 gnd |
| subject_GND | (DE-588)4173571-7 |
| title | The Pauli exclusion principle origin, verifications, and applications |
| title_auth | The Pauli exclusion principle origin, verifications, and applications |
| title_exact_search | The Pauli exclusion principle origin, verifications, and applications |
| title_full | The Pauli exclusion principle origin, verifications, and applications Ilya G. Kaplan (Materials Research Institute, National Autonomous University of Mexico, Mexico) |
| title_fullStr | The Pauli exclusion principle origin, verifications, and applications Ilya G. Kaplan (Materials Research Institute, National Autonomous University of Mexico, Mexico) |
| title_full_unstemmed | The Pauli exclusion principle origin, verifications, and applications Ilya G. Kaplan (Materials Research Institute, National Autonomous University of Mexico, Mexico) |
| title_short | The Pauli exclusion principle |
| title_sort | the pauli exclusion principle origin verifications and applications |
| title_sub | origin, verifications, and applications |
| topic | Pauli exclusion principle fast Quantum theory fast SCIENCE / Energy bisacsh SCIENCE / Mechanics / General bisacsh SCIENCE / Physics / General bisacsh Quantentheorie Pauli exclusion principle Quantum theory Pauli-Prinzip (DE-588)4173571-7 gnd |
| topic_facet | Pauli exclusion principle Quantum theory SCIENCE / Energy SCIENCE / Mechanics / General SCIENCE / Physics / General Quantentheorie Pauli-Prinzip |
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