CFU

7

Length

14 Weeks

Semester DD

Second

with Enrico Perfetto

Analytical Mechanics: Lagrange and Hamilton equations.

Quantum Mechanics: Crisis of classical physics. Introduction to the Postulates of Quantum Mechanics through the description of experiments with single photons and experiments with the polaroid. Postulates of Quantum Mechanics, superposition principle, observables, transition probabilities, operators associated with observables, average values, compatible observables, uncertainty principle, quantization postulate. Harmonic oscillator, operators of creation and annihilation, energy levels. Representation theory, Schroedinger representation. The Schrödinger equation for one-dimensional systems, the free particle, the harmonic oscillator, wells and potential barriers. Tunnel effect. Time evolution. The angular momentum and the commutators rules. The orbital angular momentum and spherical harmonics. Spin and composition of angular moments. Particle in a central field, energy levels of the hydrogenoid atoms and eigenfunctions. Time-independent perturbation theory, degenerate and non-degenerate cases, and time-dependent perturbation theory.

Statistical Mechanics: Statistical bases of thermodynamics and ensemble theory.

LEARNING OUTCOMES: The aim of the course is to introduce the student, by means of a theoretical description, to the experiments that have marked the crisis of classical physics and the physical intuitions that led to laying the foundations and developing Quantum Mechanics. It is in this context that we can understand the dynamical, electronic, optical or transport properties of materials. The main educational objectives are the search for eigenvalues and eigenvectors of simple Hamiltonians, such as two-level systems, the quantum harmonic oscillator in one and two dimensions, hydrogen atom, one-dimensional systems such as quantum wells and potential barriers, and finally systems with spin composition. Students will also be able to evolve the wave function over time. In addition, the time-independent perturbation theory, degenerate and non-degenerate cases, and time-dependent, up to the derivation of the Fermi golden rule will also be treated. Short hints are also needed on Analytical Mechanics and Statistical Mechanics, respectively in the opening and closing of the course.

KNOWLEDGE AND UNDERSTANDING:

The theoretical and practical lessons focus on the mathematical derivation and physical interpretation of the postulates of Quantum Mechanics and the resolution of simple models, in order to be able to work on systems with more elaborate Hamiltonians. The course aims to provide the student with the basic tools necessary to solve the Hamiltonian of one of the problems mentioned in the training objectives, knowing how to evolve the wave functions