Approximation Methods - Overview of Time-Independent Perturbation Theory; Interaction (or Dirac’s) representation of quantum mechanics; Time evolution of quantum states: applications to neutrino oscillations; time dependent perturbation theory (instantaneous, periodic, adiabatic); Fermi Golden Rule; Widths of states in quantum transitions; Applications to the interaction with classical electromagnetic field:photoelectric effect; WKB method and applications to Bohr-Sommerfeld quantization, finite double well potential and tunneling processes.

Theory of Angular Momemntum and Spin - Overview of angular momentum and spin eigenstates and commutation relations; Rotations operator; Additions of Angular momenta and spins.

Foundations of Quantum Mechanics - Density Matrix formalism, pure and mixture ensembles of quantum states; Einstein-Podolsky-Rosen (EPR) paradox; Einstein's locality principle and Bell's inequality for spin correlation measurements.

Scattering Theory - Lippmann-Schwinger equation; Scattering amplitude and differential cross section; Born approximation; Expansion in partial waves and phase shifts; Low energy scattering and bound states; Elastic and inelastic scattering; Inelastic electron-atom scattering and form factors; Resonant scattering for non-relativistic interacting systems; exercises. Response and correlations functions, dynamical susceptibility and spectral representation.

Primer of Quantum Theory for the electromagnetic field - Schroedinger equation in a external e.m. field and gauge invariance; Bohm-Ahranov effect and magnetic monopole; simplified approach to the quantization of electromagnetic field; spontaneous radiative emission and dipole transitions.

Path-Integrals - Propagators and Green-functions; Path-Integral formulation of quantum mechanics; Examples: free particle, harmonic oscillators; primer on instantons.

Relativistic Quantum Mechanics - Klein-Gordon Equation and Klein’s paradox; Casimir effect; Dirac Equation and the free particle and anti-paticle solutions; Weyl and Majorana representations; Non-relativistic reduction of Dirac equation: Pauli equation; Charge, Parity and Time reversal simmetries; Dirac particle in a Coulomb field; hyperfine structure and Lamb-shift; exercises.

1) J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, Ed. Addison-Wesley.

2) F. Schwabl, Advanced Quantum Mechanics, Ed. Springer.

3) Giuseppe Nardulli - Meccanica quantistica: applicazioni, vol II, Ed. Franco Angeli.

4) J.J. Sakurai, Advanced Quantum Mechanics, Ed. Addison-Wesley.

5) J.D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics, Ed. McGraw-Hill.

6) B. R. Holstein, Topics in Advanced Quantum Mechanics, Ed. Addison- Wesley.