The first half of this unit deals with the general methods of Lagrange and Hamilton, a reformulation of classical mechanics in a way that provides new and very general methods of solution, new insights into the physics, and establishes connections between classical and quantum mechanics. Topics covered include Lagrange's equation, cyclic coordinates, symmetry and conservation laws, Hamilton's equations, Poisson brackets and Hamilton's principle.
In the second half of the unit, attention is turned to statistical mechanics, a theory whose main aim is to describe the thermodynamic properties of macroscopic systems in terms of the behaviour of the immense number of particles (atoms) of which they are constituted. The kinetic theory of gases provides the starting point, but then the unit moves on to the introduction of ideas of probability and statistics, Boltzmann's statistical interpretation of entropy, the partition function, the statistical properties of identical particles embodied in Maxwell-Boltzmann statistics, Bose-Einstein statistics, and Fermi-Dirac statistics. Illustrative examples, including the recently observed phenomenon of Bose-Einstein condensation, the properties of the microwave background radiation left over from the Big Bang, and electrons in metals, will be included.
