Einstein's Other Theory

Name: Einstein's Other Theory | The Planck-Bose-Einstein Theory of Heat Capacity
Brand: Princeton University Press
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The Planck-Bose-Einstein Theory of Heat Capacity

Donald W. Rogers(Autor*in)

Princeton University Press

1. Auflage

Erschienen am 21. Juli 2020

200 Seiten

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978-0-691-21640-9 (ISBN)

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Inhalt

Cover Page
Half-title Page
Title Page
Copyright Page
Dedication Page
Contents
Preface
One: History
1.1 Failure of the Dulong-Petit Law
1.2 Crystals: Einstein's View
Problems
Two: Background
2.1 Classical Harmonic Motion
2.2 Wave Equations: The Vibrating String
2.3 Wave Motion
2.4 Solving the Wave Equation: Separation of Variables
2.5 The Time-Independent Wave Equation X(x)
2.6 The Time-Dependent Wave Equation T(t)
2.7 Superpositions
2.8 ATwo-Dimensional Wave Equation
2.9 The Time-Independent Wave Functions X(x1) and X(x2)
2.10 AThree-Dimensional Wave Equation
2.11 The Boltzmann Distribution
2.12 Degrees of Freedom
2.13 Kinetic Energy per Degree of Freedom
2.14 Boltzmann's Constant
2.15 The Translational Energy
2.16 The Energy of a Vibrational State Is
2.17 Trouble Brewing
Problems
Three: Experimental Background
3.1 Thermal Radiation in a Chamber or Cavity
3.2 Kirchhoff's Law: Absorptivity
3.3 The Intensity of Radiation
3.4 The Stefan-Boltzmann Law: Emissivity
3.5 Stefan's Law
3.6 The Blackbody Radiation Spectrum
3.7 Measurement of the Blackbody Spectrum
3.8 Astrophysical Data from the COBE Satellite
Problems
Four: The Planck Equation
4.1 The Paschen-Wien Law
4.2 Fitting the Curve
4.3 The Number Density of Oscillatory Modes
4.4 The Rayleigh-Jeans Equation
4.5 The Planck Equation
4.6 Immediate Deductions from Planck's Law
Problems
Five: The Einstein's Equation
5.1 The Einstein Model
5.2 Einstein's First Derivation: The Heat Capacity of Diamond
5.3 The Einstein Temperature
5.4 Difficulties with the Einstein Theory
Problems
Six: The Debye Equation
6.1 The Debye Model
6.2 The Debye Equation
6.3 The Debye Temperature
6.4 The Integral D
6.5 Very-Low-Temperature Behavior of the Debye Equation
6.6 The Speed of Sound in Solids
6.7 The Debye Third-Power Law
6.8 Third-Law Entropies
Problems
Seven: Quantum Statistics
7.1 The Photoelectric Effect
7.2 The Photon Gas
7.3 Bose's Letter to Einstein
7.4 The Quantum Harmonic Oscillator
7.5 The Total Vibrational Energy
7.6 Heat Capacity
7.7 Bosons and Fermions
7.8 Permutations and Combinations
7.9 Configurations
7.10 Stirling's Approximation
7.11 Constraints
7.12 The Classical Boltzmann Distribution
7.13 Fine Structure
7.14 The Classical Case: AMore General Derivation
7.15 Fermi-Dirac Counting
7.16 The Fermi-Dirac Distribution Function
7.17 Bose-Einstein Counting
7.18 The Bose-Einstein Statistical Weights WB
7.19 The Bose-Einstein Distribution Function
7.20 Summary Equations
7.21 An Alternative Derivation for Fermions and Bosons
7.22 Fermions (Again)
7.23 Bosons (Again)
7.24 Reduction to the Classical Case
7.25 The Entropy
7.26 ANote from Classical Thermodynamics: The Fundamental Equation
Problems
Eight: Consequences of the Fermi-Dirac Distribution
8.1 The Electron Gas
8.2 The Fermi Sea
8.3 The Fermi Distribution
8.4 The Electronic Contribution to Solid-State Heat Capacity
8.5 The Ground State of a Fermi Gas
8.6 The Number of Orbitals in the Ground State
8.7 The Total Energy of Electrons in the Ground State
8.8 The Density of States
8.9 The Energy of an Electron Gas
8.10 The Low-Temperature Heat Capacity of an Electron Gas
8.11 The Debye-Sommerfeld Equation
Problems
Nine: Consequences of the Bose-Einstein Distribution
9.1 Of Waves and Particles
9.2 Bose: The Density of Photon Modes
9.3 Why Is = 0 for Photons?
9.4 Phonons
9.5 The Influence of Symmetry Numbers on Rotational Spectroscopy
9.6 The Vibrational Partition Function
9.7 The Rotational Partition Function
9.8 Symmetry Numbers
9.9 Bosons, Fermions, and Triplets
9.10 The Einstein Coefficients
9.11 Lasers
9.12 The Bose-Einstein Condensation
9.13 The Bose-Einstein Condensation of Metal Vapor (Nobel Prize, 2001)
9.14 Ballistic Expansion
9.15 Macroscopic Quantum Effects
9.16 Superfluidity
9.17 Order Parameters
9.18 Superconductivity
9.19 Stopped Light
9.20 Vortices
Problems
Bibliography
Index

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