The Pauli Exclusion Principle (eBook)

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.

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