34657 - Superior Mathematical Physics

Academic Year 2009/2010

  • Docente: Sandro Graffi
  • Credits: 12
  • SSD: MAT/07
  • Language: Italian
  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)

Course contents

Mathematical formulation of the most elementary notions of quantum mechanics

1. Short survey on linear operators in Hilbert space.
2. Self-adjoint operators and elements of spectral theory.
3. Elementary description of the principles of quantum mechanics.
4. The Weyl quantization.
5. The Schroedinger equation. Self-adjointness of the Schroedinger operator.
6. Some examples: harmonic oscillator, the Zeeman effect.
7. Perturbation theory of the eigenvalues.

Introduction to statistical mechanics.

1. Elementary kinetic theory. The Maxwell distribution.
2. The Boltzmann equation and the H theorem.
3. Conservation laws and detivation of the equation of motions of the continuous media.
4. Equilibrium statistical mechanics: statistical ensembles, thermodynamic limit.
5. Phase transitions.
6. Curie-Weiss model for the magnetic phase transitions.
7. The Ising model.

Readings/Bibliography

S.Graffi, Alcuni aspetti matematici della meccanica quantistica, Quaderno INDAM-GNFM, 2004.

G.Gallavotti, Trattatello di Meccanica statistica, Quaderno INDAM-GNFM 32, 1997.

Office hours

See the website of Sandro Graffi