Chapter 16
Statistical Physics

Probabilities

Discrete outcomes
Coin tosses
Quantum coins
Coin distribution function
Dice casting
Quantum dice
Shared birthdays
approximated
N objects taken n at a time
Related to binomial distribution
Binomial distribution applet

Partition Functions

Definition
Partitions of 2 and 6
Levels
Multiplicities
Calculations
continued
Results
Comparison of distributions
BE and FD give MB
Extended application

Distribution functions

Definition
Binomial distribution
Stirling's approximation
Stirling to higher accuracy
Poisson limit
Gaussian limit
Differences between Poisson and Gaussian
Maximum likelihood and least squares
Horse/mule kick data
von Bortkiewicz
The Baker distribution
Binomial distribution applet
Poisson distribution applet
The median isn't the message

Measures of distribution

Median, mean, mode, std
Poisson example
Poisson example 2
Gaussian

Continuous Probabilities

Integration
Dice casting
continued

Maxwell-Boltzmann Distribution

Normalization and temperature
Applet I
Applet II
Average values
Gamma functions
Tabulation
Calculation
RMS, mean, and most probable
Graphical representation

Phase Space Factors

EBK quantization
Degeneracy of momenta for a given energy
Phase space
Photons and electrons
continued

Distribution Functions


Detailed balancing
Distributions

Bose Statistics

Continuum radiation

Wien and Stefan-Boltzmann laws
Blackbody radiation
Photon gas
Continuous average
Discrete average
Einstein formulation
In modern quantities
Bose
Rayleigh-Jeans
Wien
Planck
Origin of the word "photon"
Quantum Reiki

Specific heats

Dulong and Petit
Experiment
Specific heats of solids
Einstein function
Debye model

Bose condensation

Cooper pairing
The Bosenova
Superfluidity
Nonlocal interaction
Physics Today article
Einstein's AB paper in Translation (pdf)

Fermi-Dirac Statistics

Comparison of distributions
Recall the BE and FD distributions
Low temperature FD
Mean energy
Sample calculation
Temperature variation of FD
Expressions for EF and Em
Example: compute shift
FD distribution at the Fermi energy
Electron excitation in FD
Fermi distribution
Compute T from Fermi distribution
Normalizing the FD distribution
Compute FD probability from T
continued

Fermi gas in metal

Charge flow
Drift and thermal speeds
Fermi speeds
Combined motions
Acceleration between collisions
Ohm's Law
Viscous drag
Mean free path and collision time
Ohm's law and thermal conductivity
The Maxwell-Boltzmann Wiedemann-Franz Law
The Fermi-Dirac Wiedemann-Franz Law

Boltzmann factors for populations

Boltzmann population
Examples
Sample problem
continued.

Dipole-dipole forces

End-on dipole
Positive charge
Negative charge
Side-on dipole
Divergence of fields
Gauss formulation
2-D projection of 4-D divergence

Extending the dimensionality

Volumes and areas
2-dimensions
3-dimensions
1- and 4-dimensions
N-D Hyperspheres
Summary
Hypercubes
Wente torus

Multipoles

3-5 dimensions
Multipoles by differentiation
Index notation tutorial (pdf)
Differentiating 1/r
Dipole field
Problem 11-11
Summary

Van der waals fluids (See Curtis, Chapter 12)

Induced dipole-dipole interaction
Ideal gas law

van der Waals gas law

Chapter 1;   Chapter 2;   Chapter 3;   Chapter 4;   Chapter 5;   Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Homepage