PORTALE DELLA DIDATTICA

PORTALE DELLA DIDATTICA

PORTALE DELLA DIDATTICA

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Introduction to the hamiltonian formulation of classical and quantum systems

01QCTKG

A.A. 2021/22

Course Language

Inglese

Degree programme(s)

Doctorate Research in Fisica - Torino

Course structure
Teaching Hours
Lezioni 20
Lecturers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Raffa Francesco Antonino Professore Ordinario IIND-03/A 20 0 0 0 6
Co-lectures
Espandi
Context
SSD CFU Activities Area context
*** N/A ***    
Date d'appello
Orario delle lezioni
Statistiche superamento esami
The aim of the course is the derivation of the Jaynes-Cummings model for the atom-photon interaction. It is a fundamental model of quantum optics, whose physical predictions have been impressively confirmed by experiments, as well as a relevant application of the hamiltonian formulation for a quantum system. In this course one arrives at the Jaynes-Cummings model using the hamiltonian approach, described in detail first in the classical realm then in the quantum one through the Dirac quantization rule; the fundamental features of the quantized electromagnetic field are also summarized.
The topics of the fundamental courses of Analysis and Physics. Basic elements of Quantum mechanics.
Classical systems: Hamilton’s principle, Lagrangian, Legendre’s transformations, Hamiltonian. Hamiltonian equations of motion in the Poisson brackets notation. Quantum systems: canonical quantization (Dirac’s rule) and Heisenberg equation of motion. Main results of the quantization of the electromagnetic field. Derivation of the Jaynes-Cummings model for the atom-photon interaction and of the physical predictions embedded in the model. Generalized Jaynes-Cummings models and their physical applications.
On site
Oral presentation - Written report presentation
P.D.2-2 - May
1) A text with the material of the lectures, including exercises and applications, is available to the PhD students. 2) Lectures and exams may be delivered with formats different from the above ones, depending on the general sanitary condition.