Non-interacting particles gases: Bose and Fermi statistics. Black body. Interaction between atoms and electromagnetic radiation; line shapes. Hydrogenic atoms; fine structure of atomic spectra; atoms in static external fields. Exchange interaction; Born-Oppenheimer separation. Crystals: direct and reciprocal lattice; Bragg's diffraction. Lattice vibrations and specific heat. Electron gas in periodic potentials: Bloch theorem, weakly-bound electrons model and energy bands.
Lev D. Landau and Evgenij M. Lifshitz. Theoretical Physics vol. 5 – Statistical Physics .
B.H. Bransden and C.J. Joachain. Physics of atoms and molecules .
N.W. Ashcroft and N.D. Mermin. Solid State Physics
Learning Objectives
Understanding of commonly observed properties of atoms, molecules and solids on the basis of quantum and statistical mechanics. Ability to quantitatively evaluate some properties of atoms and solids, Critical understanding of books and scientific papers discussing topics related with the Physics of Matter.
Prerequisites
Courses required: Mathematical Analysis II, Analytical mechanics, Physics II
Recommended courses: Quantum Mechanics
Teaching Methods
52 hours of class lectures supplemented by exercises - 6 CFU
Further information
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Type of Assessment
Exam modality: oral examination in front of a blackboard; the exam will last 45 minutes, on average. The student will be asked to discuss 2-3 specific topics, in order to test his/her knowledge of the three main blocks of the program (non-interacting particle systems, atoms and radiation-matter interaction, elements of solid state physics). The student will be required to prove her/his knowledge of the different physical phenomena treated in the course, and should also be able to describe and reproduce proofs and calculations; she/he should also be able to estimate the order of magnitude of the different relevant physical quantities and to discuss the physical motivation of possible approximations employed in the calculations. Simple numerical exercises can complement the discussion.
The final marks will result according to the proven mastery of the discussed subjects and the ability to use a proper language.
Course program
Ideal classical gas and weakly degenerate quantum gases; Fermi gas at T=0; degenerate Bose gas and Bose condensation. Classical and quantum harmonic oscillators. Electromagnetic field at thermal equilibrium and black-body radiation. Semiclassical theory of atom-e.m. field interaction; line shapes. Hydrogenic atoms: relativistic corrections, fine structure; Zeeman and Stark effects. Two- and many-electrons atoms; exchange energy. Born-Oppenheimer separation and adiabatic approximation. Crystals: direct and reciprocal lattice; diffraction experiments. Lattice vibrations and specific heat of insulators. Electrons in crystal lattices: Bloch theorem; weakly bound electrons; origin of energy gap and energy bands.