化学の理論<br>The Theories of Chemistry

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化学の理論
The Theories of Chemistry

  • ウェブストア価格 ¥27,420(本体¥24,928)
  • Elsevier Science Ltd(2003/11発売)
  • 外貨定価 UK£ 126.50
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  • ポイント 1,245pt
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  • 製本 Hardcover:ハードカバー版/ページ数 570 p.
  • 言語 ENG
  • 商品コード 9780444514912
  • DDC分類 541.2

基本説明

Based on the argument that the needs of chemistry are distinctive, a mathematical structure of topics such as quantum mechanics, relativity theory, thermodynamics and statistical mechanics, suiting the needs of chemistry, is outlined.

Full Description

"Theories of Chemistry" reviews the theories that underpin chemistry, but yet are not traditionally recognized as such, being normally considered as part of physics. Based on the argument that the needs of chemistry are distinctive, a mathematical structure of topics such as quantum mechanics, relativity theory, thermodynamics and statistical mechanics, suiting the needs of chemistry, is outlined. The subject matter is arranged in a sequence that reveals the foundations of chemistry. Starting from the mathematical basis, the sequence runs through the general concepts (mechanics and wave formalism) and the elementary building blocks, to molecules and macrosystems. The book is the product of the author's reading of original literature rather than of standard texts. It differs from what is conventionally emphasized because of the different approach that it argues for the recognition of chemistry as an emergent discipline, ultimately based on the properties and structure of space and time.
Hence the emphasis on otherwise unexpected topics such as quaternions, lie groups, polarized light, compressed atoms, Rydberg atoms, solitons, molecular hydrogen, and phase transitions, amongst others. The topic is the understanding of chemistry from first principles. The book is self-contained and can be used without reference to other sources.

Table of Contents

Preface                                            v
1 Basic Mathematics 1 (54)
1.1 Elemenatary Vector Algebra 1 (12)
1.1.1 Vectors 1 (1)
1.1.2 Sum of Vectors 2 (1)
1.1.3 Scalar Product 2 (1)
1.1.4 Three-dimensional Vectors 3 (2)
1.1.5 Vector Product 5 (2)
1.1.6 Three-vector products 7 (1)
1.1.7 Complex Numbers 8 (2)
1.1.8 N-dimensional Vectors 10 (2)
1.1.9 Quaternions 12 (1)
1.2 Determinants and Matrices 13 (12)
1.2.1 Introduction 13 (1)
1.2.2 Matrix Operations 14 (2)
1.2.3 Inverse of a Matrix 16 (2)
1.2.4 Linear Homogeneous Equations 18 (3)
1.2.5 Linear Transformations 21 (3)
1.2.6 Direct Sums and Products 24 (1)
1.3 Vector Fields 25 (13)
1.3.1 The Gradient 26 (1)
1.3.2 The Laplacian 26 (1)
1.3.3 The Divergence 27 (1)
1.3.4 The Curl 28 (2)
1.3.5 Orthogonal Curvilinear Coordinates 30 (4)
1.3.6 Tensor Analysis 34 (4)
1.4 Differential Equations 38 (17)
1.4.1 Series Solution of Differential 39 (8)
Equations
1.4.2 Separation of Variables 47 (1)
1.4.3 Special Functions 48 (7)
2 Group Theory 55 (42)
2.1 Introduction 55 (2)
2.2 The Multiplication Table 57 (1)
2.3 Conjugate Elements and Classes 58 (1)
2.4 Homomorphism 58 (1)
2.5 Some examples of symmetry groups 59 (5)
2.5.1 Cayley's theorem 63 (1)
2.6 Field and Space 64 (7)
2.6.1 Unitary Space 65 (5)
2.6.2 Hilbert Space examples 00
2.6.3 The Eigenvalue Problem 70 (1)
2.7 Representation of Groups 71 (13)
2.7.1 Equivalent representations 72 (1)
2.7.2 Reducible Representations 72 (3)
2.7.3 Orthogonality 75
2.7.4 Orthogonal Relationships 20 (63)
2.7.5 Direct Product Representations 83 (1)
2.8 Continuous Groups (Lie Groups) 84 (13)
2.8.1 Representations of a Lie group 88 (1)
2.8.2 Important Lie Groups 88 (6)
2.8.3 Homomorphism of SU(2) with 0(3) 94 (3)
3 Particles and Waves 97 (30)
3.1 Introduction 97 (2)
3.2 Review of Classical Dynamics 99 (1)
3.3 Hamilton's Principle 100(5)
3.3.1 Lagrangian Density 102(1)
3.3.2 The Hamiltonian Function 103(2)
3.4 Hamilton-Jacobi Theory 105(2)
3.5 Potential Theory 107(4)
3.6 Wave Motion 111(16)
3.6.1 Harmonic Waves 113(1)
3.6.2 Fourier Series 114(1)
3.6.3 Fourier Transforms 115(5)
3.6.4 Wave Packets 120(2)
3.6.5 Solitons 122(3)
3.6.6 The Eikonal Equation 125(2)
4 Space and Time 127(50)
4.1 Introduction 127(2)
4.2 The Electromagnetic Field 129(11)
4.2.1 Units 130(1)
4.2.2 The Maxwell Equations 130(2)
4.2.3 Electromagnetic Potentials 132(5)
4.2.4 Electromagnetic Waves 137(3)
4.3 Special Relativity 140(19)
4.3.1 Introduction 140(3)
4.3.2 The Lorentz Transformation 143(14)
4.3.3 Physical Interpretation of Special 157(2)
Relativity
4.4 General Relativity 159(5)
4.5 Gauge Fields 164(11)
4.5.1 The Higgs Field 170(5)
4.6 The Arrow of Time 175(2)
5 Quantum Theory 177(84)
5.1 Basic Concepts 177
5.1.1 Polarized Light: A familiar example 177(4)
of quantum behaviour
5.1.2 Electron Spin 181(3)
5.1.3 Quantum States 184(1)
5.1.4 Observables 185(2)
5.1.5 Mean Values 187(1)
5.1.6 Eigenvectors 188(1)
5.1.7 Incompatibility 189(3)
5.1.8 Matrix Mechanics 192(2)
5.1.9 Quantum Particles 194(1)
5.1.10 Stationary States 195(1)
5.2 Wave Mechanics 196(23)
5.2.1 The Hydrogen Atom 201(18)
5.3 Relativistic Wave Equations 219(13)
5.3.1 Dirac's Equation 221(11)
5.4 Angular Momentum and Spin 232(13)
5.4.1 Measurement of Angular Momentum 232(1)
5.4.2 General Theory 233(4)
5.4.3 Schr inger's Equation and Spin 237(4)
5.4.4 Addition of Angular Momenta 241(2)
5.4.5 Exclusion Principle 243(2)
5.5 Quantum Mechanics of the Photon 245(16)
5.5.1 Introduction 245(1)
5.5.2 The Quantized Field 246(3)
5.5.3 Energy 249(2)
5.5.4 Momentum 251(1)
5.5.5 Polarization 252(6)
5.5.6 Spherical Waves 258(3)
6 Quantum Chemistry 261(72)
6.1 Introduction 261(1)
6.2 Quantum Aspects of General Chemistry 262(18)
6.2.1 The Equipartition Principle 263(17)
6.3 Molecular Spectroscopy 280(19)
6.3.1 The Raman effect 283(2)
6.3.2 Electronic spectra 285(1)
6.3.3 Spin Resonance Spectroscopy 286(3)
6.8.4 Optical Rotation Spectroscopy 289(3)
6.3.5 M sbauer Spectroscopy 292(1)
6.3.6 Symmetry Aspects 293(4)
6.3.7 Spectroscopic selection rules 297(2)
6.4 Free-Particle Models 299(34)
6.4.1 Particle in a Sphere 300(3)
6.4.2 Electron Gas 303(5)
6.4.3 Potential Barriers 308(4)
6.4.4 The Tunnel Effect 312(9)
6.4.5 The Nearly-free electron model 321(4)
6.4.6 Delocalized Chemical Systems 325(8)
7 Atoms and Molecules 333(74)
7.1 Many-particle Systems 333(3)
7.1.1 Two-body Systems 334(1)
7.1.2 Particles with spin 335(1)
7.2 Approximation Methods 336(9)
7.2.1 Time-dependent Perturbation 339(4)
7.2.2 The Variational Method 343(2)
7.3 Atomic Structure 345(15)
7.3.1 Many-electron Atoms 348(502)
7.3.2 Compressed Atoms 850
7.4 Molecular Systems 360(47)
7.4.1 The Born-Oppenheimer Approximation 361(2)
7.4.2 The H2+ Molecule 363(12)
7.4.3 The Hydrogen Molecule 375(3)
7.4.4 Polyatomic Molecules 378(2)
7.4.5 The LCAO-MO-SCF Method 380(6)
7.4.6 B ke Molecular-Orbital (HMO) Theory 386(6)
7.4.7 The Extended H kel Method 392(2)
7.4.8 Density Functional Theory 394(4)
7.4.9 Molecular Geometry 398(9)
8 Macrosystems 407(90)
8.1 Introduction 407(1)
8.2 Thermodynamics 408(20)
8.2.1 Theoretical Formulation 410(1)
8.2.2 Equilibrium Thermodynamics 411(7)
8.2.8 Thermodynamic Potentials 418(4)
8.2.4 Irreversible Thermodynamics 422(6)
8.3 Mechanics of Macrosystems 428(23)
8.3.1 Classical Systems 430(55)
8.3.2 Statistical Mechanics 485
8.3.3 Equilibrium Systems 438(5)
8.3.4 Statistics and Thermodynamics 443(8)
8.4 Quantum Statistics 451(34)
8.4.1 The Quantum Formalism 452(9)
8.4.2 The Density Matrix 461(2)
8.4.3 Macroscopic Variables 463(2)
8.4.4 Axioms of the Theory 465(1)
8.4.5 Symmetry Considerations 466(5)
8.4.6 The Microcanonical Ensemble 471(3)
8.4.7 The canonical ensemble 474(4)
8.4.8 The grand canonical ensemble 478(5)
8.4.9 Generalized Ensembles 483(2)
8.5 Non-equilibrium Statistical Mechanics 485(12)
8.5.1 The fluctuation-dissipation theorem 487(5)
8.5.2 Chemical Reaction 492(5)
9 Chemical Change 497(26)
9.1 Introduction 497(1)
9.2 Phase Change 498(3)
9.3 Disorder 501(10)
9.3.1 Thermodynamics of Disorder 503(1)
9.3.2 Landau Theory 504(3)
9.3.3 The Van der Waals Equation 507(4)
9.4 The Scaling Hypothesis 511(2)
9.5 Renormalization Group 513(5)
9.6 Chemical Reaction 518(3)
9.7 Conclusion 521(2)
Bibliography 523(6)
Index 529