Master Degree


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First semester
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Language of instruction: 

Italian; in English upon request.

Learning outcomes of the course unit

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.


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 contents summary

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.

Course contents

Table of contents – Programma esteso

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) 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) 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

4) 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)

5) Stationary scattering theory – Teoria di scattering stazionaria
a) Partial waves – Onde parziali
b) Optical theorem – Teorema ottico
c) Green function and Born approximation – Funzione di Green e approssimazione di Born
d) Scattering length – Lungezza di scattering

6) 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

7) Introduction to quantum fields – Introduzione nei campi quantistici
a) Photons -- Fotoni
b) Canonical field quantization – Quantizzazione canonica dei campi

Recommended readings

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; homework corrected by the lecturer. Generally, all students are expected to check on the platform Elly the available material and the indications provided by the instructor. The lectures will as a tendency take place in situ at the physics department, with possible integrations also online, in particular some exercises and their presentations. The ways of teaching may possibly change during the year in response to the pandemic situation.

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 with presentation in the lecture room 50% and oral term exam 50%) or 2) one single written final exam of duration 2-3 hours. Please see the Italian version for further details.

Other informations

Distribuzione documenti per studenti frequentanti e non frequentanti via la piattaforma ELLY.