Elements of Classical and Quantum Physics

Physical theories, fundamental constants and the role of Mathematics.- Analytical Mechanics.- Dirac's delta.- Green's functions for Electromagnetism.- Equilibrium Thermodynamics.- Classical Statistical Mechanics.- Relativity.- Particles and waves from classical to Quantum Mechanics.- Schroedinger equation.- Elementary solutions in one dimension.- Postulates and formulations of Quantum Mechanics.- Separation of variables.- Angular momentum-Hydrogen atom.- Discrete models.- Fano resonances and Green's functions.- Spin.- Quantum statistics and many-body phenomena.- Non-equilibrium phenomena and quantum transport.- Berry Phase.- Quantum Statistical Mechanics.- Entanglement, EPR paradox. Teleportation.- Perturbation theory.- Variational method in Quantum Mechanics.- Recursion methods.- Mathematical appendices: Tensors - Hermite and Laguerre Polynomials.