Group and phase speed. Crisis of classical mechanics and beginning of quantum mechanics Introduction of Schroedinger equation Operators in Hilbert spaces: bounded operators, adjoint of an operator, selfadjoint operators, weak derivative. Eigenfuncions of the Schroedinger operator. Regularity of the eigenfunctions of the Schroedinger operator Examples: free particle, potential well, harmonic oscillator, idrogen atom. Axioms of quantum mechanics. Integrals of motion. Indetermination principle.
Hamiltonian Formalism Classical Statistical Mechanics and Statistical ensembles: grand canonical, canonical and microcanonical Thermodynamic quantities in perfect gases and equivalence Specific heat for a gas of diatomic molecules Specific heat of solids and equipartition Van-Hove theorem on the existence of thermodynamic limit Tonks Gas Spin systems and phase transitions Exact solution of the Ising model in one dimension Exact solution of the Ising model with infinite range Quantusm statistical mechanics: bosons and fermions Fermi-Dirac statistics, Fermi surface, specific heat Bose-Einstein statistics Bose Condensation Black body radiation and specific heat of phonons