Learning objectives
• learning skills/communication skills: describe the fundamental concepts of quantum physics and the relevant theoretical methods
• making judgements: solve problems in advanced nonrelativistic quantum physics
• knowledge and understanding: apply the relevant theoretical methods to model concrete physical situations
Prerequisites
This course requires a knowledge of an introductory course on classical and quantum mechanics during the B.Sc. degree in physics or related fields.
Course unit content
Please refer to the extended program.
Full programme
1) Introduction – Introduzione
a) The Hamiltonian formalism of classical mechanics – Il formalismo Hamiltoniano della meccanica
classica
b) The formalism of quantum mechanics (review via handout) – Il formalismo della meccanica quantistica
(ripassata, vedi le dispense)
c) Semiclassical Theory WKB, link between classical and quantum mechanics – Teoria semiclassica WKB,
collegamento meccanica classica e quantistica
2) Light-matter interactions – Interazione luce-materia
a) Atoms in external fields (NMR, 2-level atom in laser field) – Atomo in un campo esterno (NMR, 2 livelli +
laser)
b) Rabi model and Rabi oscillations – Modello e oscillazioni di Rabi
c) Time-dependent perturbation theory – teoria di perturbazione tempo-dipendente
d) Recall of Fermi-Golden-Rule – Ricapitolazione della regola d’oro di Fermi
3) Symmetries in quantum mechanics – Simmetrie nella meccanica quantistica
a) Introduction to groups and their representations – Introduzione nella teoria dei gruppi e delle loro
rappresentazioni
b) Wigner’s theorem and connection between symmetries and quantum mechanics — Teorema di Wigner e
connesso tra simmetrie e la meccanica quantistica
c) Continuous symmetries (space-time translations, rotations, .) – Simmetrie continue (traslazioni spazio
temporali, rotazioni, .)
d) Discrete symmetries (Inversion P e T, .) – Simmetrie discrete (inversione P e T, .)
e) Applications: selection rules, gauge transforms, crystal symmetries, Bloch theorem (discrete spatial
translation symmetry), Angular momentum and spin (addition of angular momenta) — applicazioni: regole
di selezione, trasformazioni di gauge, simmetrie nei cristalli, teorema di Bloch (simmetria di traslazione
spaziale discreta), momento angolare e lo spin (somma di momenti angolari)
4) Identical particles – Particelle identiche
a) (Anti)Symmetrization – (Anti)simmetrizzazione
b) Permutation groups – Gruppi di permutazioni
c) Second quantization – La seconda quantizzazione
d) Nonrelativistic many-body quantum mechanics – Meccanica quantistica non relativistica a molti corpi
e) Evolution law – Legge di evoluzione temporale
The following chapter 5) represents specific applications of the previous ones 2) - 4) – Il capitolo seguente 5)
rappresenta applicazioni specifiche dei capitoli precedenti 2) - 4):
5) Applications - Applicazioni
a) Mean-field approximations – Approssimazioni di campo medio
b) Theory of molecules – Teoria delle molecole
c) Bose e Fermi Hubbard modells – Modello di Bose e Fermi Hubbard
d) Linear-response theory – Teoria di risposta lineare
e) Stationary scattering theory – Teoria di scattering stazionaria
f) Second quantization of photon field – Seconda quantizzazione del campo dei fotoni
Bibliography
General textbooks:
J. J. Sakurai & J. Napolitano, Modern Quantum Mechnics (Addison-Wesley, 2011)
F. Schwabl, Quantum Mechanics (Springer, 2007, 4th edition)
F. Schwabl, Advanced Quantum Mechanics (Springer 2008, 4th edition)
Books on special topics:
M. Chaichian, R. Hagedorn, Symmetries in Quantum Mechanics: From Angular Momentum to Supersymmetry (IOP, 1998)
D. J. Griffiths, Introduction to Quantum Mechanics (Pearson, 2014)
M. Le Bellac, Quantum Physics (CUP, 2006)
E. Onofri, C. Destri, Istituzioni di Fisica Teorica (Carocci, 1996)
P. Caldirola, R. Cirelli, G. M. Prosperi, Introduzione alla fisica teorica (UTET, 1982)
Teaching methods
Lectures and exercises; homework corrected by the lecturer and discussed during the lectures. The students are directly involved in the exciserses and their presentation. Generally, all students are expected to check on the platform Elly the available material and the indications provided by the instructor.
Assessment methods and criteria
Please refer to the Italian version for precise instructions. Homework exercises are given and corrected. Positively evaluated presentations of their solutions lead to 1 or maximally 2 points of bonus for the final grade. At the end of the course a written exam is given where no material can be used. The final grade takes into account the possibile bonus from the homework presentations.
Other information
Distribution of documents and course registrations via the platform ELLY of the course.
