First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
ANALYTICAL MECHANICS
SC03105660, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course First cycle degree in
MATHEMATICS
SC1159, Degree course structure A.Y. 2008/09, A.Y. 2019/20
N0
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination ANALYTICAL MECHANICS
Website of the academic structure http://matematica.scienze.unipd.it/2019/laurea
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction Italian
Branch PADOVA
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

Lecturers
Teacher in charge ANTONIO PONNO MAT/07

Mutuating
Course unit code Course unit name Teacher in charge Degree course code
SC03105660 ANALYTICAL MECHANICS ANTONIO PONNO SC1158

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/07 Mathematical Physics 6.0

Course unit organization
Period First semester
Year 3rd Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Lecture 6.0 48 102.0 No turn

Calendar
Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2008 course timetable

Syllabus
Prerequisites: Differential and integral calculus for real functions of one or more variables; basic linear algebra and geometry; Newtonian and Lagrangian mechanics.
Target skills and knowledge: The student will become acquainted with the mathematical structure and the methods of classical and quantum Hamiltonian mechanics, with a particular attention to their physical relevance.
Examination methods: Written test, including exercises and theory.
Assessment criteria: Evaluation of the ability to solve exercises and to report on a theoretical issue in a complete way.
Course unit contents: - Elements of Lagrangian mechanics; action principle; symmetries and conservation laws; gauge invariance.
- Hamilton equations, general properties. Poisson bracket. Symplectic structure and symplectic transformations.
- Action principle, canonical transformations
and Hamilton-Jacobi equation.
- Integrable systems. Liouville theorem. Arnol'd theorem and action-angle variables. Separable systems. Bohr-Sommerfeld first quantum theory.
- Hamiltonian systems as dynamical systems on a Poisson algebra.
General properties. Canonical transformations and canonicity of Hamiltonian flows.
- The Schrodinger equation and the Hamiltonian structure of quantum mechanics. The algebraic structure of quantum mechanics.
- Hamiltonian perturbation theory. Normal form. The averaging theorem.
Planned learning activities and teaching methods: Taught classes, on the blackboard, including theory and exercises.
Additional notes about suggested reading: Lecture notes available on the homepage of the lecturer.
Further references can be suggested on demand.
Textbooks (and optional supplementary readings)

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