[2025]
[ Sapienza, University of Rome ]
Program:
Lecture 1 - Statistical mechanics. Boltzmann postulate; microcanonical and canonical ensembles; example of canonical ensemble for a perfect gas; thermodynamical potentials; derivation of grand canonical ensemble; introduction to quantum statistical mechanics; quantistic definition of entropy; example of harmonic oscillator in the quantum case (and classical limit).
Lecture 2 - Quantum Mechanics I. Suggestions on how to prepare the exams for the first semester; harmonic oscillator and its properties; creation and destruction operators; infinite potential well; time evolution and match with Hamilton equations; example on computation of time evolution of a state.
Lecture 3 - Quantum Mechanics II. Perturbation theory independent from time; computation of first-order correction of the energy in perturbation and in the wave function (cases where the unperturbed state is non-degenerate or n-th degenerate); recall of Pauli principle and definition of bosons and fermions; example of harmonic oscillator in 2D with Pauli principle and perturbation theory; introduction to Classical Field theory with the example of a spring of athoms.
Notes (in italian):