D1. Knowledge and understanding: This course introduces students to the fundamentals of condensed matter physics, providing a solid foundation for understanding the physical properties of materials at the microscopic level.

D2. Applying knowledge and understanding: Students will apply quantum mechanical concepts, previously acquired in abstract form, to the study of real physical systems such as atoms, molecules, and solids. Emphasis will be placed on bridging theoretical knowledge with practical applications.
D3. Making judgements: The course offers an overview of the numerical approximations commonly used in atomic and molecular physics and develops the physical insight necessary to critically assess their validity. Students will gain the ability to make informed judgments about the appropriateness and limitations of different modeling approaches.
D4. Communication skills: Students will acquire the analytical tools needed to clearly and effectively describe the microscopic origins of macroscopic material properties, both in written and oral form, using precise scientific language.
D5. Learning skills: The course provides a broad overview of condensed matter physics, equipping students with the foundational knowledge and methodological skills necessary for tackling more advanced topics in the field.

Fundamentals of Electrodynamics and quantum physics.

The course will take place according to the following guidelines: after a review of quantum mechanics, we will "build" matter increasing gradually the level of complexity. Starting from a review of hydrogen atoms (single electrons), we will build multi-electron atoms. With them we will build the chemical bond that will be introduced and discussed first for simple molecules (diatomics) and then for more complex molecular systems.
In the second part of the course these notions will be instrumental to introduce the description of condensed-matter properties.

First part of the course: H. Haken, H.C. Wolf, Atomic and Quantum Physics. B.H.Brandsen, C.J. Joachain, Physics of atoms and molecules" (Prentice Hall). Second Parte: S. Simon, The Oxford Solid State Basics (Oxford University Press). Supplementary reading: C. Kittel, Introduction to Solid State Physics (Wiley). N. Ashcroft, D. Mermin, Solid-State Physics (Harcourt).

First Part.
After the introduction to the foundational experiments of atomic and molecular physics, the periodic table of elements and the first models for the hydrogen atom, we will structure a formalism for atomic and molecular physics as follows. We will review some concepts in quantum mechanics, in one-dimensional systems, the harmonic oscillator and its coherent states, the angular momentum operator and the spherical harmonics. The SPIN operators and the total angular momentum operator will be discussed and will be used for the construction of eigenfunctions of the energy eigenstates of the hydrogen atom. We will discuss the fine and hyperfine structure of the hydrogen atomic energy levels by perturbatively introducing relativistic corrections (spin orbit). We will discuss the interaction between an electric field and single-electron atoms, absorption and emission, and selection rules. The quantization of the electromagnetic field and the shift of Lamb.
We will recall the concept of indistinguishable particles in quantum mechanics to derive the statistical properties of fermions and bosons, and then derive the eigen-estates of 2-electron atoms in the limit of independent particles described using the spin wave functions for two electrons and the singlet and triplet spatial wavefunction. We will introduce interacting particles and the concept of screening which will remove the degeneracy of the energy eigentstes through the exchange integral. We will introduce multi-electron atoms in central potential, the Slater determinant, the Pauli exclusion principle, the electron gas and Hartree Fock method, LS and JJ coupling for angular moments and terms notation.
We will further introduce basic concepts in molecular physics treating diatomic molecules. We will explicitly calculate the stability and the energy eigenstate of molecular ion H2+ and neutral H2. We will introduce bonding and anti-bonding orbitals and the Born-Hoppenheimer approximation. We will review the origin of the chemical bond, ionic bond and covalent, for diatomic molecules. We will perform representative calculation using the LCAO method for atomic orbitals and calculate vibrational excitations in diatomic systems.

Second Part.
Crystal structure: crystal lattices, primitive cell, and reciprocal lattice.
Diffraction of X-rays, electrons, and neutrons: diffraction conditions, Bragg’s law, and relationships with the crystal structure.
Bonding in crystalline solids: main types of bonding (ionic, covalent, metallic, van der Waals) and their impact on material properties.
Lattice vibrations: phonons, phonon density of states, and their role in the thermal properties of solids (specific heat, thermal conductivity).
The Drude model for electrical conduction and electronic transport in metals.
Electrons in solids: free electron gas and behavior in the presence of periodic potentials. Bloch functions and the formation of electronic band structure. Tight-binding approach and nearly-free electrons approach.
Electronic properties of solids: electrical conductivity and thermal conductivity.

Lectures on theoretical concepts alternated with problem-solving sessions aimed at reinforcing learning.

Final written exam consisting of numerical exercises and theoretical questions on the topics covered during the course, with a possible additional oral exam. Maximum duration: 2 hours and 30 minutes. The assessment procedures will be explained to students by the instructors during the presentation of the course in the first lecture. The final grade will be expressed on a scale of 30 points. A passing grade (18/30) will be awarded to students who demonstrate a basic understanding of the main topics of the course and of the relevant technical language, as well as a limited but adequate ability to apply theoretical knowledge to practical cases. The highest grade (30 with honours) will be awarded to students who demonstrate excellent knowledge of the topics, mastery of technical language, strong analytical skills, and the ability to successfully apply theoretical knowledge to practical situations.