Mathematical Physics 3

A.Y. 2017/2018
9
Max ECTS
89
Overall hours
SSD
MAT/07
Language
Italian
Learning objectives
An introduction to the theory and mathematics of Quantum Mechanics
and Statistical Physics, both classical and quantum.
Expected learning outcomes
Basic notions of analysis, physics, geometry and probability.
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
Course syllabus
Quantum mechanics:

Group and phase speed. Crisis of classical mechanics and beginning of
quantum mechanics
Introduction of Schroedinger equation
Operators in Hilbert spaces: bounded operators, adjoint of an
operator, selfadjoint operators, weak derivative.
Eigenfuncions of the Schroedinger operator.
Regularity of the eigenfunctions of the Schroedinger operator
Examples: free particle, potential well, harmonic oscillator, idrogen
atom.
Axioms of quantum mechanics. Integrals of motion. Indetermination
principle.


Statistical mechanics:

Hamiltonian Formalism
Classical Statistical Mechanics and Statistical ensembles: grand canonical, canonical and microcanonical
Thermodynamic quantities in perfect gases and equivalence
Specific heat for a gas of diatomic molecules
Specific heat of solids and equipartition
Van-Hove theorem on the existence of thermodynamic limit
Tonks Gas
Spin systems and phase transitions
Exact solution of the Ising model in one dimension
Exact solution of the Ising model with infinite range
Quantusm statistical mechanics: bosons and fermions
Fermi-Dirac statistics, Fermi surface, specific heat
Bose-Einstein statistics
Bose Condensation
Black body radiation and specific heat of phonons
MAT/07 - MATHEMATICAL PHYSICS - University credits: 9
Practicals: 44 hours
Lessons: 45 hours
Professor(s)
Reception:
on (e-mail) appointment
office in Dept. of Mathematics