Statistical & quantum physics

At the end of this learning unit, the student is able to :

1. To explain the postulated and basic equations of the non-relativistic QM including the measure theory.
2. To apply MQ to the treatment of different simple systems.
3. To compute the mean values of simple observables for wavefunctions with one electron, their fluctuations, to check Heisenberg uncertainty relationship, and to build the matrix representation of an operator.
4. To build a molecular orbital diagram for a simple specific molecule, and to deduce from it the physical characteristics (bond order, total spin).
5. To explain the basic principles of statistical physics.
6. To compute the thermodynamical properties of a perfect gas, and to use Maxwell-Boltzmann statistics.
7. To work with the different statistical formalisms : microcanonical (e.g. study lattice specific heat - Einstein model), canonical (e.g. Debye model), and  grand-canonical (e.g. to derive Fermi-Dirac and Bose-Einstein statistics)
8. To predict the temperature-dependent behaviour of systems (specfic heat, internal energy, mean number of particules, superfuildity, superconductivity) thanks to statistical ensembles.