Mathematical Physics 3
A.Y. 2025/2026
Learning objectives
The course aims at providing the basic notions of Hamiltonian, Statistical and Quantum mechanics.
Expected learning outcomes
Undersatnding of fundamentals notions of Hamiltonian, Statistical and Quantum mechanics and ability of solving simple problems on these topics.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
Part I: Supplements of Classical and Hamiltonian Mechanics
- Review on rigid body
- Integrable cases of the rigid body
- Hamilton-Jacobi theory, separation of variables
- Brief notes on Lie algebras
- Foundations of algebraic theory of (super)integrable systems
Part II: Quantum Mechanics
- Crisis of classical mechanics
- Review of Hilbert spaces and Fourier transform
- Basic elements of linear operator theory
- Analysis of quantum systems: free particle, harmonic oscillator, hydrogen atom, double square well potential, Landau levels
- Brief notes on algebraic theory of Quantum Mechanics
- Review on rigid body
- Integrable cases of the rigid body
- Hamilton-Jacobi theory, separation of variables
- Brief notes on Lie algebras
- Foundations of algebraic theory of (super)integrable systems
Part II: Quantum Mechanics
- Crisis of classical mechanics
- Review of Hilbert spaces and Fourier transform
- Basic elements of linear operator theory
- Analysis of quantum systems: free particle, harmonic oscillator, hydrogen atom, double square well potential, Landau levels
- Brief notes on algebraic theory of Quantum Mechanics
Prerequisites for admission
Hamiltonian Mechanical Part: Rigid Body, Lagrange and Hamilton Equations.
Quantum Mechanics Part: Basic Notions of Measure Theory, L^p Spaces, Hilbert Spaces, Series and Fourier Transforms.
Quantum Mechanics Part: Basic Notions of Measure Theory, L^p Spaces, Hilbert Spaces, Series and Fourier Transforms.
Teaching methods
Front lectures in presence.
Teaching Resources
Part I:
O. Babelon, D. Bernard e M. Talon. Introduction to classical integrable systems, 2003.
A. Goriely. Integrability and Nonintegrability of Dynamical Systems, 2001.
A. Kirillov. An introduction to Lie groups and algebras, 2008.
E. T. Whittaker. A treatise on the analytical dynamics of particles and rigid bodies, 1937.
Part II:
- Bergfinnur Duurhus, Jan Philip Solovej: Mathematical Physics, lecture notes
- Emmanuel Kowalski: Spectral theory in Hilbert spaces (Lecture Notes ETH Zürich, FS 09)
- Mathieu Lewin,: Spectral theory and Quantum Mechanics (2024)
- Gerald Teschl: Mathematical Methods in Quantum Mechanics, With Applications to Schrödinger Operators
- Alessandro Teta: A Mathematical Primer on Quantum Mechanics (2018)
- Bernd Thaller: Advanced Visual Quantum Mechanics (2005)
O. Babelon, D. Bernard e M. Talon. Introduction to classical integrable systems, 2003.
A. Goriely. Integrability and Nonintegrability of Dynamical Systems, 2001.
A. Kirillov. An introduction to Lie groups and algebras, 2008.
E. T. Whittaker. A treatise on the analytical dynamics of particles and rigid bodies, 1937.
Part II:
- Bergfinnur Duurhus, Jan Philip Solovej: Mathematical Physics, lecture notes
- Emmanuel Kowalski: Spectral theory in Hilbert spaces (Lecture Notes ETH Zürich, FS 09)
- Mathieu Lewin,: Spectral theory and Quantum Mechanics (2024)
- Gerald Teschl: Mathematical Methods in Quantum Mechanics, With Applications to Schrödinger Operators
- Alessandro Teta: A Mathematical Primer on Quantum Mechanics (2018)
- Bernd Thaller: Advanced Visual Quantum Mechanics (2005)
Assessment methods and Criteria
The exam consists of two oral parts to be done together or separately. At the exam, simple exercises will be requested for solution and theory developed during the course.
MAT/07 - MATHEMATICAL PHYSICS - University credits: 9
Practicals: 48 hours
Lessons: 45 hours
Lessons: 45 hours
Professors:
Giacomelli Emanuela Laura, Gubbiotti Giorgio
Professor(s)
Reception:
Tuesday 2.30PM-4.30PM
Diparimento di Matematica "Federigo Enriques" Room 1040