Muutke küpsiste eelistusi

E-raamat: Pauli Exclusion Principle - Origin, Verifications, and Applications: Origin, Verifications, and Applications [Wiley Online]

(Universidad Nacional Autonoma de Mexico)
  • Formaat: 250 pages
  • Ilmumisaeg: 30-Dec-2016
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 111879530X
  • ISBN-13: 9781118795309
  • Wiley Online
  • Hind: 148,02 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
  • Formaat: 250 pages
  • Ilmumisaeg: 30-Dec-2016
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 111879530X
  • ISBN-13: 9781118795309
This is the first scientic 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.
Preface xi
1 Historical Survey
1(24)
1.1 Discovery of the Pauli Exclusion Principle and Early Developments
1(10)
1.2 Further Developments and Still Existing Problems
11(14)
References
21(4)
2 Construction of Functions with a Definite Permutation Symmetry
25(25)
2.1 Identical Particles in Quantum Mechanics and Indistinguishability Principle
25(4)
2.2 Construction of Permutation-Symmetric Functions Using the Young Operators
29(7)
2.3 The Total Wave Functions as a Product of Spatial and Spin Wave Functions
36(14)
2.3.1 Two-Particle System
36(5)
2.3.2 General Case of N-Particle System
41(8)
References
49(1)
3 Can the Pauli Exclusion Principle Be Proved?
50(14)
3.1 Critical Analysis of the Existing Proofs of the Pauli Exclusion Principle
50(6)
3.2 Some Contradictions with the Concept of Particle Identity and their Independence in the Case of the Multidimensional Permutation Representations
56(8)
References
62(2)
4 Classification of the Pauli-Allowed States in Atoms and Molecules
64(42)
4.1 Electrons in a Central Field
64(10)
4.1.1 Equivalent Electrons: L-S Coupling
64(7)
4.1.2 Additional Quantum Numbers: The Seniority Number
71(1)
4.1.3 Equivalent Electrons: j--j Coupling
72(2)
4.2 The Connection between Molecular Terms and Nuclear Spin
74(8)
4.2.1 Classification of Molecular Terms and the Total Nuclear Spin
14(65)
4.2.2 The Determination of the Nuclear Statistical Weights of Spatial States
79(3)
4.3 Determination of Electronic Molecular Multiplets
82(24)
4.3.1 Valence Bond Method
82(5)
4.3.2 Degenerate Orbitals and One Valence Electron on Each Atom
87(4)
4.3.3 Several Electrons Specified on One of the Atoms
91(2)
4.3.4 Diatomic Molecule with Identical Atoms
93(5)
4.3.5 General Case I
98(2)
4.3.6 General Case II
100(4)
References
104(2)
5 Parastatistics, Fractional Statistics, and Statistics of Quasiparticles of Different Kind
106(29)
5.1 Short Account of Parastatistics
106(3)
5.2 Statistics of Quasiparticles in a Periodical Lattice
109(12)
5.2.1 Holes as Collective States
109(2)
5.2.2 Statistics and Some Properties of Holon Gas
111(6)
5.2.3 Statistics of Hole Pairs
117(4)
5.3 Statistics of Cooper's Pairs
121(3)
5.4 Fractional Statistics
124(11)
5.4.1 Eigenvalues of Angular Momentum in the
Three- and Two-Dimensional Space
124(4)
5.4.2 Anyons and Fractional Statistics
128(5)
References
133(2)
Appendix A Necessary Basic Concepts and Theorems of Group Theory
135(26)
A.1 Properties of Group Operations
135(6)
A.1.1 Group Postulates
135(2)
A.1.2 Examples of Groups
137(1)
A.1.3 Isomorphism and Homomorphism
138(1)
A.1.4 Subgroups and Cosets
139(1)
A.1.5 Conjugate Elements. Classes
140(1)
A.2 Representation of Groups
141(20)
A.2.1 Definition
141(1)
A.2.2 Vector Spaces
142(3)
A.2.3 Reducibility of Representations
145(2)
A.2.4 Properties of Irreducible Representations
147(1)
A.2.5 Characters
148(1)
A.2.6 The Decomposition of a Reducible Representation
149(2)
A.2.7 The Direct Product of Representations
151(3)
A.2.8 Clebsch--Gordan Coefficients
154(2)
A.2.9 The Regular Representation
156(1)
A.2.10 The Construction of Basis Functions for Irreducible Representation
157(3)
References
160(1)
Appendix B The Permutation Group
161(21)
B.1 General Information
161(6)
B.1.1 Operations with Permutation
161(3)
B.1.2 Classes
164(1)
B.1.3 Young Diagrams and Irreducible Representations
165(2)
B.2 The Standard Young-Yamanouchi Orthogonal Representation
167(15)
B.2.1 Young Tableaux
167(3)
B.2.2 Explicit Determination of the Matrices of the Standard Representation
170(3)
B.2.3 The Conjugate Representation
173(2)
B.2.4 The Construction of an Antisymmetric Function from the Basis Functions for Two Conjugate Representations
175(1)
B.2.5 Young Operators
176(2)
B.2.6 The Construction of Basis Functions for the Standard Representation from a Product of N Orthogonal Functions
178(3)
References
181(1)
Appendix C The Interconnection between Linear Groups and Permutation Groups
182(35)
C.1 Continuous Groups
182(7)
C.1.1 Definition
182(3)
C.1.2 Examples of Linear Groups
185(2)
C.1.3 Infinitesimal Operators
187(2)
C.2 The Three-Dimensional Rotation Group
189(12)
C.2.1 Rotation Operators and Angular Momentum Operators
189(2)
C.2.2 Irreducible Representations
191(3)
C.2.3 Reduction of the Direct Product of Two Irreducible Representations
194(3)
C.2.4 Reduction of the Direct Product of k Irreducible Representations. 3n - j Symbols
197(4)
C.3 Tensor Representations
201(13)
C.3.1 Construction of a Tensor Representation
201(1)
C.3.2 Reduction of a Tensor Representation into Reducible Components
202(5)
C.3.3 Littlewood's Theorem
207(2)
C.3.4 The Reduction of U2j +1 → R3
209(5)
C.4 Tables of the Reduction of the Representations Uγ2j+,1 to the Group R3
214(3)
References
216(1)
Appendix D Irreducible Tensor Operators
217(6)
D.1 Definition
217(3)
D.2 The Wigner-Eckart Theorem
220(3)
References
222(1)
Appendix E Second Quantization
223(5)
References
227(1)
Index 228
Ilya G. Kaplan, Head of Department, Materials Research Institute, National Autonomous University of Mexico, Mexico Ilya Kaplan has been studying the Pauli Exclusion Principle for more than 35 years and is a well-known scientist in this field. He has published 4 books in Russian, 4 books in English, including the Wiley title Intermolecular Interactions, and 11 book chapters, one of which was devoted to the Pauli Exclusion Principle. He was also an Associate Editor for Wiley's Handbook of Molecular Physics and Quantum Chemistry, published in 2003.