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 corse is supposed to be adequate for a curriculum for a Master degree in Physics.
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
1. Introduction – Introduzione
1.1. Newton’s revolution in classical mechanics – La rivoluzione di Newton nella meccanica classica
1.2. 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. Semiclassics – Teoria semiclassica
2.1. Old quantum theory – La vecchia teoria quantistica
2.2. WKB(J) – WKB
2.3. EKB quantization – EKB
3.4. Feynman path integrals – I cammini di Feynman
4. Perturbation theory – Teoria delle perturbazioni
4.1. Rayleigh-Schrödinger (time-independent PT)
4.2. Other methods: Variational ansatz, Hartree, Thomas-Fermi – Metodi approssimativi
4.3. Time-dependent perturbation theory – La teoria delle perturbazioni dipendenti al tempo
5. Symmetries in quantum mechanics – Simmetrie nella meccanica quantistica
5.1. Introduction to groups – Introduzione nella teoria dei gruppi
5.2. Gauge transforms – Trasformazioni di gauge
5.3. Discrete and continuous symmetries – Simmetrie discrete e continue
5.4. Bloch theorem – Teorema di Bloch
5.5. Angular momentum and spin – Momento angolare e lo spin
6. Stationary scattering theory – Teoria di scattering stazionaria
7. Identical particles – Particelle identiche
7.1. (Anti)Symmetrization – (Anti)simmetrizzazione
7.2. Second quantization – La seconda quantizzazione
7.3. Nonrelativistic many-body quantum mechanics – Meccanica quantistica non relativistica di multi corpi
7.4. Mean-field approximations – Approssimazioni di campo medio
7.5. Heitler-London method – Metodo di Heitler e London (esercizio)
8. Open quantum systems – Sistemi quantistici aperti
8.1. The measurement concept and problem – Il concetto di misura
8.2. Density operator – Operatore densità
8.3. Master equation for density operator – Master equation per l’operatore di densità
9. Quantum information in a nutshell – Breve introduzzione nella teoria quantistica dell’informazione
9.1. Entanglement
9.2. EPR and GHZ paradoxa (entanglement) – I paradossi di EPR e GHZ
9.3. Mini introduction to quantum computing – mini introduzione alla computazione quantistica
10. Introduction to noninteracting quantum fields (optional chapter) – Introduzione nei campi quantistici senza interazioni (capitolo facoltativo)
10.1. Photons -- Fotoni
10.2. Canonical field quantization – Quantizzazione canonica dei campi
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. Mini seminars by the students in class.
Assessment methods and criteria
For the exam grade we will take an average over the student's contributions during the course and his final exam grad. Details are given in the Italian version.
Other information
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