Chapter 5b - Quantum Statistical Mechanics

Partition Functions

  • Definition
  • Case study
  • Partitions of 2 and 6
  • Multiplicities
  • Calculations
  • continued
  • Results
  • Comparison of distributions
  • Krane's omission
  • Extended application
  • FD temperature variation

    • Phase Space Factors

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

    • Distribution Functions

  • Enhancement factor
  • Detailed balancing
  • Distributions
  • Dist. functions
  • (BE+FD)/2 = MB

    • Bose Statistics

    Blackbody radiation

  • Photon gas
  • Wien and Stefan-Boltzmann laws
  • Brick size

    Specific heats

  • Dulong and Petit
  • Experiment
  • Specific heats of solids
  • Einstein function

    • Fermi-Dirac Statistics

  • Comparison of distributions
  • Temperature variation of FD
  • Electron excitation in FD
  • MB and FD thermal speeds









  • Recall the BE and FD distributions
  • Distribution or probability?
  • Normalization by adjustment of EF
  • Normalization
  • Low temperature FD
  • Mean energy
  • Sample calculation (P10-17)
  • FD distribution at the Fermi energy

    Bose condensation

  • Cooper pairing
  • The Bosenova
  • Superfluidity
  • Nonlocal interaction

  • Blackbody radiation
  • Integrals and sums
  • Continuous average
  • Discrete average
  • Euclid's theorem
  • Book IX, Prop. 35
  • Brick size
  • Rayleigh-Jeans
  • Wien
  • Planck
  • Statistics formulation
  • Einstein formulation
  • In modern quantities
  • Physics Today article
    Applications and implications

  • Power from the Sun
  • The Greenhouse Effect
  • Solar cells
  • 2.7 degree BBrad
  • Distribution

    • Maxwell-Boltzmann Distribution

  • Applet I
  • Applet II
  • Normalization and temperature
  • Mode, mean, RMS
  • Graphical representation

    • Assignment:
        Problems 9, 14, 15.
  • Problem 10-9a,   10-9b,     Problem 10-14,     Iteration ,     Problem 10-15
    Perception of continuous and discrete radiation

  • Full-spectrum solar cells
  • 3-color vision
  • Color confusion
  • Who has the handicap?
    Assignment:
    Problems 14, 15

    Assignment:
    Problems 17, 21, 23.
  • 10-17     10-21a   10-21b     10-23

    • Boltzmann factors for populations

  • Boltzmann population
  • Examples

    • Stellar Classifications

    The puzzle

  • Temperature definitions
  • The grand fact
  • Fr. Angelo Secchi
  • The Vatican observatory
  • August Comte on stellar composition
  • Kirchhoff & Bunsen on stellar composition
  • Stellar classifications
  • Relation to temperature

    • The solution

  • The Ladies of Observatory Hill
  • Group photo
  • Annie Cannon and Cecilia Payne
  • Sir Arthur Eddington
  • Anecdotes
  • Henry Norris Russell and Lyman Spitzer
  • Iron?
  • Relation to temperature
  • Study of H and K lines
  • Cosmic abundances
  • Bar graph










    • Distribution functions

  • Definition
  • Binomial distribution
  • Stirling to higher accuracy
  • Poisson limit
  • Gaussian limit
  • Differences between Poisson and Gaussian
  • Horse/mule kick data
  • von Bortkiewicz
  • The Baker distribution

    • Measures of distribution

  • Median, mean, mode, std
  • Poisson example
  • Poisson example 2
  • Gaussian
  • The median isn't the message

    • Assignment:
      Problems 1, 2).
  • Problem 10-2     plot
    • Assignment:
      Questions 1, 2, 5, 6;   Problems 2, 4, 5