ADVANCED QUANTUM MECHANICS

Acquisire una conoscenza approfondita della meccanica quantistica inclusa la sua estensione relativistica. In particolare l'obiettivo e' conoscere i principali metodi di approssimazione per risolvere problemi inerenti a sistemi fisici di interesse per la fisica moderna come anche l'approccio quantistico al processo di scattering. Accedere a formulazioni piu' avanzate della meccanisca quantistica quali la seconda quantizzazione per trattare sistemi di bosoni e fermioni e la formulazione della meccanica quantistica in termini di integrali di Feynmann.

Istituzioni di Fisica Teorica della Laurea Triennale in Fisica

Non obbligatoria ma fortemente consigliata.

Approximation Methods

Overview of Time-Independent Perturbation Theory; Interaction (or Dirac’s) representation of quantum mechanics; time dependent perturbation theory (instantaneous, periodic, adiabatic); Fermi Golden Rule; Applications to the interaction with classical electromagnetic field and photoelectric effect; Berry's geometrical phase;WKB method and applications to Bohr-Sommerfeld quantization, finite double well potential and tunneling processes; Eikonal approximation; exercises.

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 and Feynmann diagrams for non-relativistic interacting systems; exercises.

Second Quantization

Identical particles, many-particle states and the formulation of quantum mechanics in second quantization; Symmetric and anti-symmetric states: bosons and fermions; One-body and two-body operators; Two-particle correlation functions for bosons and fermions; Hanburry-Twiss effect; weakly interacting Bose gas and Gross-Pitaevskii equation.

Primer of Quantum Theory for the electromagnetic field

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

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

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

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

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

5) P. Roman, Advanced Quantum Theory, Ed. Addison-Wesley.

L'esame prevede sia una prova scritta di risoluzione di esercizi di meccanica quantistica che una prova orale sui diversi argomenti del programma.

Vedi esercizi svolti in classe e gia' assegnati negli ultimi anni del corso.

Gli esercizi principalmente saranno sulla teoria perturbativa dipenendente e/o indipendente dal tempo, sul metodo WKB, sulla teoria dello scattering.