
Course unit
HAMILTONIAN MECHANICS
SCL1000251, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/07 
Mathematical Physics 
6.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
2 MATHEMATICAL PHYSICS 
01/10/2018 
30/11/2019 
ROSSI
PAOLO
(Presidente)
PONNO
ANTONIO
(Membro Effettivo)
FASSO'
FRANCESCO
(Supplente)

Prerequisites:

Basics of algebra and differential geometry (the very basics of differential geometry will be recalled at the beginning of the course, if needed).
Basic knowledge of Hamiltonian mechanics and/or quantum mechanics would help putting the course content into context, but is not strictly needed. 
Target skills and knowledge:

By the end of the course the student should be able to navigate the technical literature on the subject and read and understand at least some of the research papers. He/She should acquire the skills necessary to solve problems by applying the notions and methods discussed in the course. 
Examination methods:

To be decided depending also on the number of students, but probably either a relatively simple written exam granting access to an oral exposition in the form of a short seminar plus some questions, or a written exam containing both simple exercises and questions on theory. 
Assessment criteria:

Evaluation will first focus on the student's acquisition of the course core material and then his/her ability to apply it to understand and possibly solve related problems. 
Course unit contents:

Hamiltonian systems in Poisson manifolds
(Poisson algebras, deformation theory, Poisson manifolds and their geometry,...).
Integrability
(reminder of ArnoldLiouville integrability, Lax representations, bihamiltonian structures,...).
Elements of quantization
(basic ideas of quantum mechanics, elements of deformation quantization, quantum mechanics in phase space,...).
Evolutionary Hamiltonian PDEs
(as infinite dimensional Hamiltonian systems, modern theory of integrable PDEs,...). 
Planned learning activities and teaching methods:

Lectures are given at the blackboard. 
Additional notes about suggested reading:

References will be given on the various topics, as the course progresses, but the lectures will be as selfcontained as possible 
Textbooks (and optional supplementary readings) 


