Academic Year 2023-2024



Paolo Giannozzi
Unit Credits
Teaching Period
First Period
Course Type
Prerequisites. Basic knowledge of classical Physics: mechanics, thermodynamics, electromagnetism, and of Mathematics: vector spaces, linear algebra, differential equations
Teaching Methods. Lectures at the blackboard
Verification of Learning. The exam consists in a homework (a problem to be solved or a dissertation on a specific argument), followed by an oral exam. In the latter, we start from the written report on the homework and explore the main topics of the course in order to verify the actual understanding of them.

More Information. Web page of the course:

At the end of the course the student is expected to

– know and understand the mathematical and physical basis of statistical mechanics and of non-relativistic quantum mechanics

– know their main applications to our understanding of the structure of matter

– be able to solve simple problems of statistical and quantum mechanics and to predict the qualitative behavior of simple systems based on the known results of statistical and quantum mechanics.

This course provides an introduction to non-relativistic quantum mechanics and to statistical mechanics. Introduction to quantum mechanics: probabilistic interpretation, time-dependent and time-independent Schroedinger equation, examples of solution of one-dimensional Schroedinger equations (free particles, wave packets, potential wells, harmonic oscillator). Algebraic solution for the harmonic oscillator. The formalism of quantum mechanics: Hilbert space, observables, properties of physical operators, generalized statistical interpretation, generalized indeterminacy principle, compatible observables, commutators, costants of motion, Dirac notation. Schroedinger equation in three dimensions for central potentials: variable separation, angular and radial quatione. Hydrogen atom. Angular momentum, commutation rules, eigenfunctions of the orbital angular momentum. Electron spin. Many-body systems. Identical particles: Pauli principle. Many-electron atoms, periodic table of the elements. Introduction to statistical mechanics Boltzmann statistics. Quantum statistics, Fermi-Dirac, Bose-Einstein. Paradoxes and interpretations of quantum mechanics: Bell inequalities. A glimpse on quantum computing.
Introduction to Quantum Mechanics, 2nd Edition, D. J. Griffiths, Prentice-Hall (Chap.1-5, 12).

Lecture notes and other texts provided during the course (in English).