دانلود کتاب Mathematical Physics

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Cover S Title List of Published Books Mathematical Physics © 2010 WILEY-VCH ISBN 978-3-527-40808-5 Contents Preface Table of Contents and Categories Constants, Signs, Symbols, and General Remarks List of Symbols 1 Vectors 1.1 Definition and Important Properties 1.1.1 Definitions 1.2 Product of a Scalar and a Vector 1.3 Position Vector 1.4 Scalar Product 1.5 Vector Product 1.6 Differentiation 1.7 Spherical Coordinates 1.8 Cylindrical Coordinates 2 Tensors and Matrices 2.1 Dyadic or Tensor Product 2.2 Cartesian Representation 2.3 Dot Product 2.3.1 Unit Tensor 2.4 Symmetric Tensor 2.5 Eigenvalue Problem 3 Hamiltonian Mechanics 3.1 Newtonian, Lagrangian and Hamiltonian Descriptions 3.1.1 Newtonian Description 3.1.2 Lagrangian Description 3.1.3 Hamiltonian Description 3.2 State of Motion in Phase Space. Reversible Motion 3.3 Hamiltonian for a System of many Particles 3.4 Canonical Transformation 3.5 Poisson Brackets References 4 Coupled Oscillators and Normal Modes 4.1 Oscillations of Particles on a String and Normal Modes 4.2 Normal Coordinates 5 Stretched String 5.1 Transverse Oscillations of a Stretched String 5.2 Normal Coordinates for a String 6 Vector Calculus and the del Operator 6.1 Differentiation in Time 6.2 Space Derivatives 6.2.1 The Gradient 6.2.2 The Divergence 6.2.3 The Curl 6.2.4 Space Derivatives of Products 6.3 Space Derivatives in Curvilinear Coordinates 6.3.1 Spherical Coordinates (r, \theta, \phi) 6.3.2 Cylindrical Coordinates 6.4 Integral Theorems 6.4.1The Line Integral of \Grad \phi 6.4.2 Stokes's Theorem 6.5 Gauss's Theorem 6.6 Derivation of the Gradient, Divergence and Curl 7 Electromagnetic Waves 7.1 Electric and Magnetic Fields in a Vacuum 7.2 The Electromagnetic Field Theory 8 Fluid Dynamics 8.1 Continuity Equation 8.2 Fluid Equation of Motion 8.3 Fluid Dynamics and Statistical Mechanics 9 Irreversible Processes 9.1 Irreversible Phenomena, Viscous Flow, Diffusion 9.2 Collision Rate and Mean Free Path 9.3 Ohm's Law, Conductivity, and Matthiessen's Rule 10 The Entropy 10.1 Foundations of Thermodynamics 10.2 The Carnot Cycle 10.3 Carnot's Theorem 10.4 Heat Engines and Refrigerating Machines 10.5 Clausius's Theorem 10.6 The Entropy 10.7 The Exact Differential Reference 11 Thermodynamic Inequalities 11.1 Irreversible Processes and the Entropy 11.2 The Helmholtz Free Energy 11.3 The Gibbs Free Energy 11.4 Maxwell Relations 11.5 Heat Capacities 11.6 Nonnegative Heat Capacity and Compressibility References 12 Probability, Statistics and Density 12.1 Probabilities 12.2 Binomial Distribution 12.3 Average and Root-Mean-Square Deviation. Random Walks 12.4 Microscopic Number Density 12.5 Dirac's Delta Function 12.6 The Three-Dimensional Delta Function 13 Liouville Equation 13.1 Liouville's Theorem 13.2 Probability Distribution Function. The Liouville Equation 13.3 The Gibbs Ensemble 13.4 Many Particles Moving in Three Dimensions 13.5 More about the Liouville Equation 13.6 Symmetries of Hamiltonians and Stationary States 14 Generalized Vectors and Linear Operators 14.1 Generalized Vectors. Matrices 14.2 Linear Operators 14.3 The Eigenvalue Problem 14.4 Orthogonal Representation 15 Quantum Mechanics for a Particle 15.1 Quantum Description of a Linear Motion 15.2 The Momentum Eigenvalue Problem 15.3 The Energy Eigenvalue Problem 16 Fourier Series and Transforms 16.1 Fourier Series 16.2 Fourier Transforms 16.3 Bra and Ket Notations 16.4 Heisenberg's Uncertainty Principle 17 Quantum Angular Momentum 17.1 Quantum Angular Momentum 17.2 Properties of Angular Momentum 18 Spin Angular Momentum 18.1 The Spin Angular Momentum 18.2 The Spin of the Electron 18.3 The Magnetogyric Ratio 18.3.1 A. Free Electron 18.3.2 B. Free Proton 18.3.3 C. Free Neutron 18.3.4 D. Atomic Nuclei 18.3.5 E. Atoms and Ions 19 Time-Dependent Perturbation Theory 19.1 Perturbation Theory 1; The Dirac Picture 19.2 Scattering Problem; Fermi's Golden Rule 19.3 Perturbation Theory 2. Second Intermediate Picture References 20 Laplace Transformation 20.1 Laplace Transformation 20.2 The Electric Circuit Equation 20.3 Convolution Theorem 20.4 Linear Operator Algebras 21 Quantum Harmonic Oscillator 21.1 Energy Eigenvalues 21.2 Quantum Harmonic Oscillator Reference 22 Permutation Group 22.1 Permutation Group 22.2 Odd and Even Permutations 23 Quantum Statistics 23.1 Classical Indistinguishable Particles 23.2 Quantum-Statistical Postulate. Symmetric States for Bosons 23.3 Antisymmetric States for Fermions. Pauli's Exclusion Principle 23.4 Occupation-Number Representation 24 The Free-Electron Model 24.1 Free Electrons and the Fermi Energy 24.2 Density of States 24.3 Qualitative Discussion 24.4 Sommerfeld's Calculations 25 The Bose-Einstein Condensation 25.1 Liquid Helium 25.2 The Bose-Einstein Condensation of Free Bosons 25.3 Bosons in Condensed Phase References 26 Magnetic Susceptibility 26.1 Introduction 26.2 Pauli Paramagnetism 26.3 Motion of a Charged Particle in Electromagnetic Fields 26.4 Electromagnetic Potentials 26.5 The Landau States and Energies 26.6 The Degeneracy of the Landau Levels 26.7 Landau Diamagnetism References 27 Theory of Variations 27.1 The Euler-Lagrange Equation 27.2 Fermat's Principle 27.3 Hamilton's Principle 27.4 Lagrange's Field Equation 28 Second Quantization 28.1 Boson Creation and Annihilation Operators 28.2 Observables 28.3 Fermions Creation and Annihilation Operators 28.4 Heisenberg Equation of Motion Reference 29 Quantum Statistics of Composites 29.1 Ehrenfest-Oppenheimer-Bethe's Rule 29.2 Two-Particle Composites 29.3 Discussion References 30 Superconductivity 30.1 Basic Properties of a Superconductor 30.1.1 Zero Resistance 30.1.2 Meissner Effect 30.1.3 Ring Supercurrent and Flux Quantization 30.1.4 Josephson Effects 30.1.5 Energy Gap 30.1.6 Sharp Phase Change 30.2 Occurrence of a Superconductor 30.2.1 Elemental Superconductors 30.2.2 Compound Superconductors 30.2.3 High-T, Superconductors 30.3 Theoretical Survey 30.3.1 The Cause of Superconductivity 30.3.2 The Bardeen-Cooper-Schrieffer Theory 30.4 Quantum-Statistical Theory 30.4.1 The Full Hamiltonian 30.4.2 Summary of the Results References 31 Complex Numbers and Taylor Series 31.1 Complex Numbers 31.2 Exponential and Logarithmic Functions 31.2.1 Laws of Exponents 31.2.2 Natural Logarithm 31.2.3 Relationship between Exponential and Trigonometric Functions 31.3 Hyperbolic Functions 31.3.1 Definition of Hyperbolic Functions 31.3.2 Addition Formulas 31.3.3 Double-Angle Formulas 31.3.4 Sum, Difference and Product of Hyperbolic Functions 31.3.5 Relationship between Hyperbolic and Trigonometric Functions 31.4 Taylor Series 31.4.1 Derivatives 31.4.2 Taylor Series 31.4.3 Binomial Series 31.4.4 Series for Exponential and Logarithmic Functions 31.5 Convergence of a Series 32 Analyticity and Cauchy-Riemann Equations 32.1 The Analytic Function 32.2 Poles 32.3 Exponential Functions 32.4 Branch Points 32.5 Function with Continuous Singularities 32.6 Cauchy-Riemann Relations 32.7 Cauchy-Riemann Relations Applications 33 Cauchy's Fundamental Theorem 33.1 Cauchy's Fundamental Theorem 33.2 Line Integrals 33.3 Circular Integrals 33.4 Cauchy's Integral Formula 34 Laurent Series 34.1 Taylor Series and Convergence Radius 34.2 Uniform Convergence 34.3 Laurent Series 35 Multivalued Functions 35.1 Square-Root Functions. Riemann Sheets and Cut 35.2 Multivalued Functions 36 Residue Theorem and Its Applications 36.1 Residue Theorem 36.2 Integrals of the Form 36.3 Integrals of the Type 36.4 Integrals of the Type Int(f(cos\theta), sin\theta),, 0, 2\pi) 36.5 Miscellaneous Integrals Appendix A Representation-Independence of Poisson Brackets Appendix B Proof of the Convolution Theorem Appendix C Statistical Weight for the Landau States Appendix D Useful Formulas References Index