{"product_id":"the-pauli-exclusion-principle-9781118795323","title":"The Pauli Exclusion Principle","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Historical Survey 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Discovery of the Pauli Exclusion Principle and Early Developments 1\u003c\/p\u003e \u003cp\u003e1.2 Further Developments and Still Existing Problems 11\u003c\/p\u003e \u003cp\u003eReferences 21\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Construction of Functions with a Definite Permutation Symmetry 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Identical Particles in Quantum Mechanics and Indistinguishability Principle 25\u003c\/p\u003e \u003cp\u003e2.2 Construction of Permutation-Symmetric Functions Using the Young Operators 29\u003c\/p\u003e \u003cp\u003e2.3 The Total Wave Functions as a Product of Spatial and Spin Wave Functions 36\u003c\/p\u003e \u003cp\u003e2.3.1 Two-Particle System 36\u003c\/p\u003e \u003cp\u003e2.3.2 General Case of N-Particle System 41\u003c\/p\u003e \u003cp\u003eReferences 49\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Can the Pauli Exclusion Principle Be Proved? 50\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Critical Analysis of the Existing Proofs of the Pauli Exclusion Principle 50\u003c\/p\u003e \u003cp\u003e3.2 Some Contradictions with the Concept of Particle Identity and their Independence in the Case of the Multidimensional Permutation Representations 56\u003c\/p\u003e \u003cp\u003eReferences 62\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Classification of the Pauli-Allowed States in Atoms and Molecules 64\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Electrons in a Central Field 64\u003c\/p\u003e \u003cp\u003e4.1.1 Equivalent Electrons: L–S Coupling 64\u003c\/p\u003e \u003cp\u003e4.1.2 Additional Quantum Numbers: The Seniority Number 71\u003c\/p\u003e \u003cp\u003e4.1.3 Equivalent Electrons: j–j Coupling 72\u003c\/p\u003e \u003cp\u003e4.2 The Connection between Molecular Terms and Nuclear Spin 74\u003c\/p\u003e \u003cp\u003e4.2.1 Classification of Molecular Terms and the Total Nuclear Spin 74\u003c\/p\u003e \u003cp\u003e4.2.2 The Determination of the Nuclear Statistical Weights of Spatial States 79\u003c\/p\u003e \u003cp\u003e4.3 Determination of Electronic Molecular Multiplets 82\u003c\/p\u003e \u003cp\u003e4.3.1 Valence Bond Method 82\u003c\/p\u003e \u003cp\u003e4.3.2 Degenerate Orbitals and One Valence Electron on Each Atom 87\u003c\/p\u003e \u003cp\u003e4.3.3 Several Electrons Specified on One of the Atoms 91\u003c\/p\u003e \u003cp\u003e4.3.4 Diatomic Molecule with Identical Atoms 93\u003c\/p\u003e \u003cp\u003e4.3.5 General Case I 98\u003c\/p\u003e \u003cp\u003e4.3.6 General Case II 100\u003c\/p\u003e \u003cp\u003eReferences 104\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Parastatistics, Fractional Statistics, and Statistics of Quasiparticles of Different Kind 106\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Short Account of Parastatistics 106\u003c\/p\u003e \u003cp\u003e5.2 Statistics of Quasiparticles in a Periodical Lattice 109\u003c\/p\u003e \u003cp\u003e5.2.1 Holes as Collective States 109\u003c\/p\u003e \u003cp\u003e5.2.2 Statistics and Some Properties of Holon Gas 111\u003c\/p\u003e \u003cp\u003e5.2.3 Statistics of Hole Pairs 117\u003c\/p\u003e \u003cp\u003e5.3 Statistics of Cooper’s Pairs 121\u003c\/p\u003e \u003cp\u003e5.4 Fractional Statistics 124\u003c\/p\u003e \u003cp\u003e5.4.1 Eigenvalues of Angular Momentum in the Three- and Two-Dimensional Space 124\u003c\/p\u003e \u003cp\u003e5.4.2 Anyons and Fractional Statistics 128\u003c\/p\u003e \u003cp\u003eReferences 133\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A: Necessary Basic Concepts and Theorems of Group Theory 135\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Properties of Group Operations 135\u003c\/p\u003e \u003cp\u003eA.1.1 Group Postulates 135\u003c\/p\u003e \u003cp\u003eA.1.2 Examples of Groups 137\u003c\/p\u003e \u003cp\u003eA.1.3 Isomorphism and Homomorphism 138\u003c\/p\u003e \u003cp\u003eA.1.4 Subgroups and Cosets 139\u003c\/p\u003e \u003cp\u003eA.1.5 Conjugate Elements. Classes 140\u003c\/p\u003e \u003cp\u003eA.2 Representation of Groups 141\u003c\/p\u003e \u003cp\u003eA.2.1 Definition 141\u003c\/p\u003e \u003cp\u003eA.2.2 Vector Spaces 142\u003c\/p\u003e \u003cp\u003eA.2.3 Reducibility of Representations 145\u003c\/p\u003e \u003cp\u003eA.2.4 Properties of Irreducible Representations 147\u003c\/p\u003e \u003cp\u003eA.2.5 Characters 148\u003c\/p\u003e \u003cp\u003eA.2.6 The Decomposition of a Reducible Representation 149\u003c\/p\u003e \u003cp\u003eA.2.7 The Direct Product of Representations 151\u003c\/p\u003e \u003cp\u003eA.2.8 Clebsch–Gordan Coefficients 154\u003c\/p\u003e \u003cp\u003eA.2.9 The Regular Representation 156\u003c\/p\u003e \u003cp\u003eA.2.10 The Construction of Basis Functions for Irreducible Representation 157\u003c\/p\u003e \u003cp\u003eReferences 160\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B: The Permutation Group 161\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 General Information 161\u003c\/p\u003e \u003cp\u003eB.1.1 Operations with Permutation 161\u003c\/p\u003e \u003cp\u003eB.1.2 Classes 164\u003c\/p\u003e \u003cp\u003eB.1.3 Young Diagrams and Irreducible Representations 165\u003c\/p\u003e \u003cp\u003eB.2 The Standard Young–Yamanouchi Orthogonal Representation 167\u003c\/p\u003e \u003cp\u003eB.2.1 Young Tableaux 167\u003c\/p\u003e \u003cp\u003eB.2.2 Explicit Determination of the Matrices of the Standard Representation 170\u003c\/p\u003e \u003cp\u003eB.2.3 The Conjugate Representation 173\u003c\/p\u003e \u003cp\u003eB.2.4 The Construction of an Antisymmetric Function from the Basis Functions for Two Conjugate Representations 175\u003c\/p\u003e \u003cp\u003eB.2.5 Young Operators 176\u003c\/p\u003e \u003cp\u003eB.2.6 The Construction of Basis Functions for the Standard Representation from a Product of N Orthogonal Functions 178\u003c\/p\u003e \u003cp\u003eReferences 181\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix C: The Interconnection between Linear Groups and Permutation Groups 182\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eC.1 Continuous Groups 182\u003c\/p\u003e \u003cp\u003eC.1.1 Definition 182\u003c\/p\u003e \u003cp\u003eC.1.2 Examples of Linear Groups 185\u003c\/p\u003e \u003cp\u003eC.1.3 Infinitesimal Operators 187\u003c\/p\u003e \u003cp\u003eC.2 The Three-Dimensional Rotation Group 189\u003c\/p\u003e \u003cp\u003eC.2.1 Rotation Operators and Angular Momentum Operators 189\u003c\/p\u003e \u003cp\u003eC.2.2 Irreducible Representations 191\u003c\/p\u003e \u003cp\u003eC.2.3 Reduction of the Direct Product of Two Irreducible Representations 194\u003c\/p\u003e \u003cp\u003eC.2.4 Reduction of the Direct Product of k Irreducible Representations. 3n − j Symbols 197\u003c\/p\u003e \u003cp\u003eC.3 Tensor Representations 201\u003c\/p\u003e \u003cp\u003eC.3.1 Construction of a Tensor Representation 201\u003c\/p\u003e \u003cp\u003eC.3.2 Reduction of a Tensor Representation into Reducible Components 202\u003c\/p\u003e \u003cp\u003eC.3.3 Littlewood’s Theorem 207\u003c\/p\u003e \u003cp\u003eC.3.4 The Reduction of U2j + 1 R3 209\u003c\/p\u003e \u003cp\u003eC.4 Tables of the Reduction of the Representations U λ 2j+1 to the Group R3 214\u003c\/p\u003e \u003cp\u003eReferences 216\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix D: Irreducible Tensor Operators 217\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eD.1 Definition 217\u003c\/p\u003e \u003cp\u003eD.2 The Wigner–Eckart Theorem 220\u003c\/p\u003e \u003cp\u003eReferences 222\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix E: Second Quantization 223\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences 227\u003c\/p\u003e \u003cp\u003eIndex 228\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406924554583,"sku":"9781118795323","price":98.06,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118795323.jpg?v=1730497578","url":"https:\/\/bookcurl.com\/products\/the-pauli-exclusion-principle-9781118795323","provider":"Book Curl","version":"1.0","type":"link"}