Learning objectives
The goal of this course is to provide the students a pretty good knowledge of the foundations and the techniques of quantum mechanics. The course is supposed to be adequate for a curriculum for a Master degree in Physics. For further details please see the Italian version.
Prerequisites
This course requires a knowledge of an introductory course on quantum mechanics during the B.Sc. degree in physics or related fields.
Course unit content
We will use a modern approach to quantum mechanics to provide a solid basis of theory in quantum physics adapted to a Master's course in physics.
Full programme
Table of contents – Programma esteso
1) Introduction (review via handout) – Introduzione (ripassata, vedi le dispense)
a) The Hamiltonian formalism of classical mechanics – Il formalismo Hamiltoniano della meccanica classica
b) The formalism of quantum mechanics – Il formalismo della meccanica quantistica
c) Extensions of Newtonian mechanics: relativity, quantum mechanics, and quantum field theory – Oltre la meccanica di
Newton: teoria relativistica, meccanica quantistica e teoria quantistica dei campi
2) Advanced Semiclassics – Teoria semiclassica avvanzata
a) EKB quantization in phase space – EKB nello spazio delle fasi
b) Feynman path integrals – I cammini di Feynman
3) Time-dependent systems – Sistemi tempo dipendenti
a) Time evolution operator – Operatore di evoluzione temporale
b) Adiabatic evolution and Berry’s phase – evoluzione adiabatica e la fase di Berry
c) Floquet systems – Sistemi di Floquet
4) Symmetries in quantum mechanics – Simmetrie nella meccanica quantistica
a) Introduction to groups – Introduzione nella teoria dei gruppi
b) Gauge transforms – Trasformazioni di gauge
c) Discrete and continuous symmetries – Simmetrie discrete e continue
d) Bloch theorem – Teorema di Bloch
e) Angular momentum and spin – Momento angolare e lo spin
5) Identical particles – Particelle identiche
a) (Anti)Symmetrization – (Anti)simmetrizzazione
b) Second quantization – La seconda quantizzazione
c) Nonrelativistic many-body quantum mechanics – Meccanica quantistica non relativistica di multi corpi
d) Example: Few sites with bosons – Esempio: bosoni in pochi siti
e) Mean-field approximations – Approssimazioni di campo medio
f) Heitler-London method – Metodo di Heitler e London (facoltativo/esercizio)
6) Introduction to noninteracting quantum fields – Introduzione nei campi quantistici senza interazioni
a) Photons -- Fotoni
b) Canonical field quantization – Quantizzazione canonica dei campi
7) Stationary scattering theory – Teoria di scattering stazionaria
a) Partial waves – Onde parziali
b) Optical theorem – Teorema ottico
c) Born-Oppenheimer approximation – Approssimazione di Born-Oppenheimer
d) Scattering length – Lungezza di scattering
8) Relativistic quantum mechanics – Meccanica quantistica relativistica
a) Klein-Gordon equation – Equazione di Klein-Gordon
b) Spin ½ – Lo spin ½
c) Dirac equation – Equazione di Dirac
9) Open systems – Sistemi aperti
a) The measurement concept and problem – Il concetto di misura
b) Density operator – Operatore densità
c) Master equation for density operator – Master equation per l’operatore di densità
10) Quantum information in a nutshell – Breve introduzzione nella teoria quantistica dell’informazione
a) Entanglement
b) EPR and GHZ paradoxa (entanglement) – I paradossi di EPR e GHZ
Bibliography
JJ Sakurai, Modern Quantum Mechnics (Addison-Wesley 2003)
F Schwabl, Quantum Mechanics (Springer 2007)
LD Landau, LM Lifschitz, Quantum Mechanics (Vol. 3, Elsevier 1977)
Book on special topics:
WKBJ/EKB/Feynman: S Wimberger, Nonlinear Dynamics and Quantum Chaos (Springer 2014)
Teaching methods
Lectures and exercises in class; homework corrected by the lecturer.
Assessment methods and criteria
The exam can be taken in two possible ways: either 1) an average over the student's contributions during the course (homeworks and term exam) or 2) one single written final exam. Please see the Italian version for further details.
Other information
- - -
