First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCL1000251, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course Second cycle degree in
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2019/20
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination HAMILTONIAN MECHANICS
Website of the academic structure
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge PAOLO ROSSI MAT/03

Course unit code Course unit name Teacher in charge Degree course code

ECTS: details
Type Scientific-Disciplinary 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 of
Individual study
Lecture 6.0 48 102.0 No turn

Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
3 MATHEMATICAL PHYSICS 01/10/2019 30/11/2020 ROSSI PAOLO (Presidente)
PONNO ANTONIO (Membro Effettivo)
2 MATHEMATICAL PHYSICS 01/10/2018 30/11/2019 ROSSI PAOLO (Presidente)
PONNO ANTONIO (Membro Effettivo)

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,...).

(reminder of Arnold-Liouville 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 self-contained as possible
Textbooks (and optional supplementary readings)