| Preface |
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xi | |
| Authors |
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xiii | |
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Chapter 1 Basic Principles of Statistical Physics |
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1 | (66) |
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1.1 Microscopic and Macroscopic Description of States |
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1 | (1) |
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2 | (1) |
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1.3 Gibbs Ergodic Assumption |
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3 | (1) |
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4 | (1) |
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1.5 Experimental Basis of Statistical Mechanics |
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5 | (1) |
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1.6 Definition of Expectation Values |
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6 | (3) |
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1.7 Ergodic Principle and Expectation Values |
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9 | (5) |
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1.8 Properties of Distribution Functions |
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14 | (2) |
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1.8.1 About Probabilities |
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14 | (1) |
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1.8.2 Normalization Requirement of Distribution Functions |
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15 | (1) |
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1.8.3 Property of Multiplicity of Distribution Functions |
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15 | (1) |
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1.9 Relative Fluctuation of an Additive Macroscopic Parameter |
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16 | (10) |
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1.9.1 Questions and Answers |
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20 | (6) |
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26 | (13) |
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1.10.1 Questions and Answers |
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30 | (9) |
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1.11 Gibbs Microcanonical Ensemble |
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39 | (5) |
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1.12 Microcanonical Distribution in Quantum Mechanics |
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44 | (4) |
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48 | (3) |
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1.14 Density Matrix in Energy Representation |
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51 | (5) |
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56 | (11) |
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1.15.1 Entropy of Microcanonical Distribution |
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58 | (2) |
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1.15.2 Exact and "Inexact" Differentials |
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60 | (1) |
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1.15.3 Properties of Entropy |
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61 | (6) |
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Chapter 2 Thermodynamic Functions |
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67 | (68) |
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67 | (5) |
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72 | (1) |
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73 | (11) |
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2.3.1 Questions on Stationary Distributions Functions and Ideal Gas Statistics |
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75 | (9) |
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2.4 Thermodynamic Identity |
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84 | (4) |
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2.5 Laws of Thermodynamics |
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88 | (5) |
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2.5.1 First Law of Thermodynamics |
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89 | (2) |
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2.5.2 Second Law of Thermodynamics |
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91 | (2) |
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2.6 Thermodynamic Potentials, Maxwell Relations |
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93 | (5) |
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2.7 Heat Capacity and Equation of State |
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98 | (2) |
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100 | (5) |
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2.9 Joule--Thomson Process |
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105 | (4) |
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109 | (4) |
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2.11 Condition for Equilibrium and Stability in an Isolated System |
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113 | (5) |
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2.12 Thermodynamic Inequalities |
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118 | (3) |
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2.13 Third Law of Thermodynamics |
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121 | (3) |
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122 | (2) |
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2.14 Dependence of Thermodynamic Functions on Number of Particles |
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124 | (5) |
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2.15 Equilibrium in an External Force Field |
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129 | (6) |
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Chapter 3 Canonical Distribution |
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135 | (54) |
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3.1 Gibbs Canonical Distribution |
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135 | (4) |
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3.2 Basic Formulas of Statistical Physics |
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139 | (21) |
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160 | (19) |
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3.4 Experimental Basis of Statistical Mechanics |
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179 | (1) |
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3.5 Grand Canonical Distribution |
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180 | (5) |
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3.6 Extremum of Canonical Distribution Function |
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185 | (4) |
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189 | (58) |
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189 | (2) |
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4.2 Boltzmann Distribution |
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191 | (5) |
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4.2.1 Distribution with Respect to Coordinates |
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195 | (1) |
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4.3 Entropy of a Nonequilibrium Boltzmann Gas |
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196 | (4) |
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4.4 Free Energy of the Ideal Boltzmann Gas |
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200 | (23) |
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4.5 Equipartition Theorem |
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223 | (4) |
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227 | (4) |
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4.7 Vibrations of Diatomic Molecules |
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231 | (4) |
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4.8 Rotation of Diatomic Molecules |
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235 | (4) |
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239 | (5) |
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4.10 Electronic Angular Momentum Effect |
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244 | (1) |
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4.11 Experiment and Statistical Ideas |
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245 | (2) |
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246 | (1) |
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Chapter 5 Quantum Statistics of Ideal Gases |
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247 | (58) |
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5.1 Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac Statistics |
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247 | (1) |
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5.2 Generalized Thermodynamic Potential for a Quantum Ideal Gas |
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248 | (1) |
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5.3 Fermi-Dirac and Bose-Einstein Distributions |
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249 | (3) |
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5.4 Entropy of Nonequilibrium Fermi and Bose Gases |
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252 | (6) |
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252 | (4) |
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256 | (2) |
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5.5 Thermodynamic Functions for Quantum Gases |
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258 | (5) |
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5.6 Properties of Weakly Degenerate Quantum Gases |
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263 | (3) |
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263 | (3) |
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5.7 Degenerate Electronic Gas at Temperature Different from Zero |
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266 | (5) |
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5.8 Experimental Basis of Statistical Mechanics |
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271 | (1) |
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5.9 Application of Statistics to an Intrinsic Semiconductor |
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272 | (7) |
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5.9.1 Concentration of Carriers |
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273 | (6) |
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5.10 Application of Statistics to Extrinsic Semiconductor |
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279 | (5) |
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284 | (4) |
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5.11.1 Condensation of Bose Gases |
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284 | (4) |
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5.12 Equilibrium or Black Body Radiation |
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288 | (6) |
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5.12.1 Electromagnetic Eigenmodes of a Cavity |
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288 | (6) |
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5.13 Application of Statistical Thermodynamics to Electromagnetic Eigenmodes |
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294 | (11) |
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Chapter 6 Electron Gas in a Magnetic Field |
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305 | (24) |
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6.1 Evaluation of Diamagnetism of a Free Electron Gas; Density Matrix for a Free Electron Gas |
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305 | (11) |
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6.2 Evaluation of Free Energy |
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316 | (2) |
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6.3 Application to a Degenerate Gas |
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318 | (2) |
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6.4 Evaluation of Contour Integrals |
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320 | (4) |
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6.5 Diamagnetism of a Free Electron Gas; Oscillatory Effect |
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324 | (5) |
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Chapter 7 Magnetic and Dielectric Materials |
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329 | (14) |
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7.1 Thermodynamics of Magnetic Materials in a Magnetic Field |
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329 | (4) |
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7.2 Thermodynamics of Dielectric Materials in an Electric Field |
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333 | (3) |
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7.3 Magnetic Effects in Materials |
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336 | (4) |
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7.4 Adiabatic Cooling by Demagnetization |
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340 | (3) |
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Chapter 8 Lattice Dynamics |
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343 | (46) |
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8.1 Periodic Functions of a Reciprocal Lattice |
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343 | (1) |
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343 | (4) |
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8.3 Vibrational Modes of a Monatomic Lattice |
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347 | (12) |
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8.3.1 Linear Monatomic Chain |
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348 | (10) |
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358 | (1) |
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8.4 Vibrational Modes of a Diatomic Linear Chain |
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359 | (5) |
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8.5 Vibrational Modes in a Three-Dimensional Crystal |
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364 | (11) |
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8.5.1 Properties of the Dynamical Matrix |
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369 | (4) |
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8.5.2 Cyclic Boundary for Three-Dimensional Cases |
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373 | (1) |
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8.5.2.1 Born--Von Karman Cyclic Condition |
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373 | (2) |
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8.6 Normal Vibration of a Three-Dimensional Crystal |
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375 | (14) |
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Chapter 9 Condensed Bodies |
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389 | (18) |
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9.1 Application of Statistical Thermodynamics to Phonons |
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389 | (2) |
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9.2 Free Energy of Condensed Bodies in the Harmonic Approximation |
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391 | (3) |
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9.3 Condensed Bodies at Low Temperatures |
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394 | (3) |
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9.4 Condensed Bodies at High Temperatures |
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397 | (1) |
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9.5 Debye Temperature Approximation |
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398 | (5) |
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9.6 Volume Coefficient of Expansion |
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403 | (2) |
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9.7 Experimental Basis of Statistical Mechanics |
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405 | (2) |
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Chapter 10 Multiphase Systems |
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407 | (14) |
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10.1 Clausius--Clapeyron Formula |
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407 | (6) |
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413 | (8) |
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Chapter 11 Macroscopic Quantum Effects: Superfluid Liquid Helium |
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421 | (14) |
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11.1 Nature of the Lambda Transition |
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421 | (3) |
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11.2 Properties of Liquid Helium |
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424 | (1) |
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11.3 Landau Theory of Liquid He II |
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425 | (5) |
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11.4 Superfluidity of Liquid Helium |
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430 | (5) |
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Chapter 12 Nonideal Classical Gases |
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435 | (14) |
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12.1 Pair Interactions Approximation |
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435 | (6) |
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12.2 Van Der Waals Equation |
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441 | (1) |
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12.3 Completely Ionized Gas |
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442 | (7) |
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Chapter 13 Functional Integration in Statistical Physics |
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449 | (70) |
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13.1 Feynman Path Integrals |
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449 | (1) |
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13.2 Least Action Principle |
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450 | (6) |
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13.3 Representation of Transition Amplitude through Functional Integration |
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456 | (17) |
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13.3.1 Transition Amplitude in Hamiltonian Form |
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460 | (3) |
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13.3.2 Transition Amplitude in Feynman Form |
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463 | (9) |
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13.3.3 Example: A Free Particle |
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472 | (1) |
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1.3.4 Transition Amplitudes Using Stationary Phase Method |
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473 | (6) |
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13.4.1 Motion in Potential Field |
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473 | (3) |
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13.4.2 Harmonic Oscillator |
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476 | (3) |
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13.5 Representation of Matrix Element of Physical Operator through Functional Integral |
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479 | (2) |
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13.6 Property of Path Integral Due to Events Occurring in Succession |
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481 | (1) |
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482 | (1) |
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13.8 Transition Amplitude for Time-Independent Hamiltonian |
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483 | (2) |
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13.9 Eigenvectors and Energy Spectrum |
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485 | (9) |
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13.9.1 Harmonic Oscillator Solved via Transition Amplitude |
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485 | (3) |
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13.9.2 Coordinate Representation of Transition Amplitude of Forced Harmonic Oscillator |
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488 | (2) |
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13.9.3 Matrix Representation of Transition Amplitude of Forced Harmonic Oscillator |
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490 | (4) |
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13.10 Schrodinger Equation |
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494 | (2) |
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13.11 Green Function for Schrodinger Equation |
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496 | (1) |
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13.12 Functional Integration in Quantum Statistical Mechanics |
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497 | (1) |
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13.13 Statistical Physics in Representation of Path Integrals |
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497 | (6) |
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13.14 Partition Function of Forced Harmonic Oscillator |
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503 | (1) |
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13.15 Feynman Variational Method |
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504 | (5) |
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13.15.1 Proof of Feynman Inequality |
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506 | (1) |
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13.15.2 Application of Feynman Inequality |
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507 | (2) |
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13.16 Feynman Polaron Energy |
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509 | (10) |
| References |
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519 | (2) |
| Index |
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521 | |