
Course unit
ANALYTICAL MECHANICS
SC03105660, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2017/18
ECTS: details
Type 
ScientificDisciplinary 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 
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 HamiltonJacobi equation.
 Integrable systems. Liouville theorem. Arnol'd theorem and actionangle variables. Separable systems. BohrSommerfeld 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) 

Sustainable Development Goals (SDGs)

