Kaplan The Pauli Exclusion Principle

Origin, Verifications, and Applications
1. Auflage 2016
ISBN: 978-1-118-79524-8
Verlag: John Wiley & Sons
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 256 Seiten, E-Book

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.

Autoren/Hrsg.

Kaplan, Ilya G.

Inhaltsverzeichnis

Preface
Chapter 1 Historical Survey
1.1. Discovery of the Pauli Exclusion Principle and early developments
1.2. Further developments and still existing problems
References
Chapter 2 Construction of Functions with a Definite Permutation Symmetry
2.1. Identical particles in quantum mechanics and indistinguishability principle
2.2. Construction of permutation-symmetrical functions using the Young operators
2.3. The total wave functions as a product of spatial and spin wave functions
2.3.1 Two-particle system
2.3.2 General case of N-particle system
References
Chapter 3 Can the Pauli Exclusion Principle Be Proved?
3.1. Critical analysis of the existing proofs of the Pauli exclusion principle
3.2. Some contradictions with the concept of particle identity and their independence in the case of the multi-dimensional permutation representations
References
Chapter 4 Classification of the Pauli-Allowed States in Atoms and Molecules
4.1. Electrons in a central field
4.1.1 Equivalent electrons. L-S coupling
4.1.2. Additional quantum numbers. The seniority number
4.1.3 Equivalent electrons. j-j coupling
4.2. The connection between molecular terms and nuclear spin
4.2.1 Classification of molecular terms and the total nuclear spin
4.2.2 The determination of the nuclear statistical weights of spatial states
4.3. Determination of electronic molecular multiplets
4.3.1 Valence bond method
4.3.2 Degenerate orbitals and one valence electron on each atom
4.3.3 Several electrons specified on one of the atoms
4.3.4 Diatomic molecule with identical atoms
4.3.5 General case I
4.3.6 General case II
References
Chapter 5 Parastatistics, Fractional Statistics, and Statistics of Quasiparticles of Different Kind
5.1. Short account of parastatistics
5.2. Statistics of quasiparticles in a periodical lattice
5.2.1 Holes as collective states
5.2.2 Statistics and some properties of holon gas
5.2.3 Statistics of hole pairs
5.3 Statistics of Cooper's pairs
5.4 Fractional statistics
5.4.1 Eigenvalues of angular momentum in the three- and two-dimensional space
5.4.2 Anyons and fractional statistics
References
Appendix 1 Necessary Basic Concepts and Theorems of Group Theory
A1.1 Properties of group operations
A1.2 Representation of groups
References
Appendix 2 The Permutation Group
A2.1 General information
A2.2 The standard Young-Yamanouchi orthogonal representation
References
Appendix 3 The Interconnection Between Linear Groups and Permutation Groups.
A3.1 Continuous groups
A3.2 The three-dimensional rotation group
A3.3 Tensor representations
A3.4 Tables of the reductions of the representation to the group R3
References
Appendix 4 Irreducible Tensor Operators
A4.1 Definition
A4.2 The Wigner-Eckart theorem
References
Appendix 5 Second Quantization
References
Index