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• The most practical ensemble is the canonical ensemble with N, V, and T fixed.
• This chapter derives the canonical ensemble, which is arguably the most important concept in quantum statistical mechanics.
• A canonical ensemble does not evolve over time, despite the fact that the underlying system is in constant motion.
• Example of canonical ensemble for a quantum system consisting of one particle in a potential well.
• A canonical ensemble for this system, for the temperature shown.
• Example of canonical ensemble for a classical system consisting of one particle in a potential well.
• The advantage of the canonical ensemble should now be apparent.
• We have derived the properties of the canonical ensemble using a Taylor expansion of the entropy.
• The grand-canonical ensemble is for "open" systems, where the number of particles, , can change.