The course aims to discuss advanced concepts of quantum mechanics and several applications relevant for the future study of condensed matter physics, many-body theory and statistical mechanics.

The student will have to manage advanced concepts like: quantum problems for identical particles, the basics of the path-integral formulation of quantum mechanics, the basics of second quantization.

The knowledge of basic concepts and tools of quantum mechanics are needed (see the topics of the ”Introduction to Quantum Mechanics” module)

1. Definition of the Propagator and Formulation of Quantum Mechanics Using Path Integrals 2. Time-Dependent Perturbation Theories 3. Identical Particles in Quantum Mechanics 4. Symmetries in Quantum Mechanics 5. The density matrix operator 6. Fermi and Bose distributions 7. Introduction to second quantization

Frontal theory lectures and classes of applications and exercises.

Dirac, P. A. M.; The Principles of Quantum Mechanics (Oxford University Press) Merzbacher, E.; Quantum Mechanics (J. Wiley & Sons, Inc.) Messiah, A.; Quantum Mechanics (Dover) Picasso, L. E.; Lectures in Quantum Mechanics (Springer) d’Emilio, E., Picasso, L. E.; Problems in Quantum Mechanics: with Solutions (Springer) Sakurai, J. J.; Modern Quantum Mechanics (Addison-Wesley)

Dispense;

Modalità di esame: Prova scritta (in aula);

Exam: Written test;

... The exam is written only, the student will be asked to solve exercises. The maximum score of the exam is 30/30, as per the Italian system.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.