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PHY 418: Statistical Mechanics I
Prof. S. Teitel stte@pas.rochester.edu  Spring 2007
Lecture Notes
My hand written class lecture notes are being scanned and uploaded for you to view. Please be warned that these are the notes I prepare for myself to lecture from  they are not in general carefully prepared for others to read. I make no guarantees about their legibility, or that they are totally free of errors. I hope, nevertheless that you will find them useful. The lectures are uploaded as pdf files, so you will need Adobe Acrobat Reader in order to read them. You can download Acrobat Reader for free here.
The lecture note files correspond roughly to the material presented in a given day's lecture. But you may on occassion find the end of one day's lecture at the start of the file for the next day's lecture, so please look there if you think there might be something missing.
 Lecture 0  Sketching the history of statistical mechanics and thermodynamics (another such page here.)
 Lecture 1  Postulates of classical thermodynamics, entropy, temperature, pressure, chemical potential
 Lecture 2  Conditions for thermal. mechanical and chemical equilibrium, concavity of the entropy, the Euler relation, equations of state, the GibbDuhem relation, entropy of the ideal gas
 Lecture 3  Energy minimum principle, Legendre transformations, Helmholtz free energy
 Lecture 4  Enthalpy, Gibbs free energy, Grand Potential, heat reservior, extrema principles for thermodynamic potentials, Maxwell's relations
 Lecture 5  Response functions (specific heat, compressibility, thermal expansion) and relations between them, stability and curvature of free energies
 Something Extra!  Heat engines and the Carnot cycle
 Lecture 6  Kinetic theory of the ideal gas, Maxwell's velocity distribution, statistical ensembles and the ergodic hypothesis
 Lecture 7  Liouville's theorem, microcanonical ensemble, density of states and number of states, connection to entropy
 Lecture 8  Entropy of the ideal gas, entropy of mixing and Gibbs paradox, indistinguishable particles, SackurTetrode equation
 Lecture 9  Canonical ensemble, energy fluctuations and specific heat, equivalence of microcanonical and canonical ensembles
 Lecture 10  Average energy vs most probably energy, proof of Stirling's formula, factorization of canonical partition function for noninteractng particles, ideal gas
 Lecture 11  Virial and equipartition theorems, elastic vibrations of solids and the Law of Dulong and Petit, paramagnetism and the Curie Law (note: the 3rd from last page of these notes is out of order  it should be the last page!)
 Lecture 12  Entropy and information theory
 Lecture 13  The grand canonical ensemble, fluctuations of energy and number of particles
 Lecture 14  The grand canonical partition function for noninteracting degrees of freedom, chemical equilibrium, adsorption sites
 Lecture 15  The density operator and quantum ensembles
 Lecture 16  Quantum many particle systems, symmetry of the wavefunction, boson and fermions, noninteracting particles
 Lecture 17  Two particle density matrix in real space, N particle partition function in real space representation, grand canonical partition function for noninteracting fermions and bosons
 Lecture 18  Average occupation numbers, comparison with and validity of the classical limit of a quantum ideal gas, the harmonic oscillator and bosons
 Lecture 19  Debye model for the specific heat due to ionic vibrations, black body radiation
 Lecture 20  Ideal quantum gas of fermions or bosons, density, pressure, energy, classical limit
 Lecture 21  Degenerate fermi gas, Sommerfeld model of electrons in a metal, Fermi energy, specific heat
 Lecture 22  Pauli paramagnetism of an ideal fermi gas
 Lecture 23  Ideal gas of bosons, BoseEinstein condensation
 Lecture 24  BoseEinstein condensation in laser cooled atomic gases, classical spin models and ensembles
 Lecture 25  Ising model, phase transitions and the thermodynamic limit, phase diagram
 Lecture 26  Mean field approximation for the Ising model, graphical solution
 Lecture 27  Critical exponents, Maxwell construction, Landau's theory of phase transitions
 Lecture 28  Critical exponents in Landau theory, exact solution of 1D Ising model
 Lecture 29  LandauGinzburg theory, correlation length, fluctuations and the upper critical dimension

