Use probability density functions to describe a system, and recognize simple probability functions and their properties including Gaussian (normal), binomial (or multinomial), and Poisson distributions.
Use combinatorics to define probabilities in simple systems.
Describe how to choose a Gibbsian ensemble for calculation of system properties. Be able to recognize when the following ensembles are appropriate: microcanonical (N,V,E), canonical (N,V,T), grand canonical (V,T,m), isobaric-isothermal (N,T,P). Know how to construct the partition function in each case.
Calculate average system quantities and thermodynamic variables using the appropriate partition function.
Calculate the size of fluctuations of system properties and relate them to the number of particles in a system.
Use proper statistics for classical particles and for quantum particles (bosons or fermions).
Calculate canonical partition functions for translation, rotation, and harmonic vibration. Use them for applications and know when they don't apply.
Explain the meaning, significance and range of applicability of these fundamentals: ergodic hypothesis, equipartition theorem, and Bose-Einstein condensation.
Use statistical mechanical principles to describe chemical equilibrium constants.
Apply statistical mechanical principles to simple crystals, blackbody radiation and imperfect gases.
Use the Metropolis Monte Carlo method to calculate statistical averages for a system. Know how to choose an efficient sampling method.
Show how to use molecular dynamics to calculate statistical averages for a molecular system. Know when molecular dynamics is more appropriate than Monte Carlo methods. Know the advantages and disadvantages of common trajectory propagation algorithms.
Obtain the radial distribution from the probability function for a system, from Monte Carlo calculations or molecular dynamics trajectories and evaluate system properties from the radial distribution function.
Use Monte Carlo and transfer matrix methods to study a system of interacting spins as a model of phase transitions.