Learning outcomes
Apply the basic principles of quantum mechanics to evaluate the electronic structure of atoms, molecules and solids, of the atomic motions in molecules and solids, of the thermodynamic properties, of the response function of those systems to external electric or magnetic fields and of the main spectroscopies used to derive the properties of atoms, molecules and solids.
Course contents
Atoms- general aspects: central field approximation, self-consistent construction of the effective potential, Hydrogenic atoms, finite nuclear mass effects, positronium, muonic and Rydberg atoms, orbital and spin magnetic moments and spin-orbit interaction, transition probabilities and selection rules
Typical atoms: Alkali atoms, Helium atom (Generalities and ground state, Excited states and the exchange interaction)
The shell vectorial model: Coupling of angular momenta, LS coupling model,the effective magnetic moment, the Hund rules for the ground state, jj coupling scheme
Atoms in electric and magnetic fields: Stark effect and atomic polarizability, Zeeman regime, Paschen-Back regime, Paramagnetism of non-interacting atoms and mean field Interaction, Atomic diamagnetism
Nuclear moments and hyperfine interactions: Magnetic hyperfine interaction - F states, electric quadrupole interaction
Spin statistics, magnetic resonance, spin motion and echoes
Molecules: general aspects: Born-Oppenheimer separation and the adiabatic approximation, Classification of the electronic states, separated-atoms and united-atoms schemes and correlation diagram
Electronic states in diatomic molecules: H2+ molecule as prototype of molecular orbital (MO) approach, bonding mechanism and the exchange of the electron , homonuclear molecules in the MO scenario, H2 as prototype of the Valence Bond (VB) approach, Comparison of MO and VB scenarios in H2 , Heteronuclear molecules and the electric dipole moment
Electronic states in selected polyatomic molecules: qualitative aspects of NH3 and H2O? molecules, bonds due to hybrid atomic orbitals, delocalization and the benzene molecule, Ammonia molecule in electric field and the Ammonia MASER
Nuclear motions in molecules and related properties: rotational motions, principles of rotational spectroscopy, thermodynamical energy from rotational motions, orientational electric polarizability, vibrational motions, principles of vibrational spectroscopy and anharmonicity effects, Morse potential, roto-vibrational eigenvalues and coupling effects, polyatomic molecules: normal modes, principles of Raman spectroscopy, electronic spectra and Franck - Condon principle, effects of nuclear spin statistics in homonuclear diatomic
molecules
Crystal structures: translational invariance, Bravais lattices and Wigner-Seitz cell, reciprocal lattice and Brillouin cell, typical crystal structures
Electron states in crystals: the band concept, the Bloch orbital, role and properties of k, periodic boundary conditions , density of states, dispersion relations and critical points, the effective electron mass, electrons in empty lattice, weakly bound electrons, tightly bound electrons
Miscellaneous aspects related to the electronic structure: bonding mechanisms and cohesive energies, Ionic crystals, Lennard-Jones interaction and molecular crystals, electron states of magnetic ions in a crystal field, simple picture of the electric transport
Vibrational motions of the ions and thermal effects: motions of the ions in the harmonic approximation, branches and dispersion relations, the case of monoatomic and diatomic one-dimensional crystals, Einstein and Debye crystals, Phonons, thermal properties related to lattice vibrations, the Mossbauer effect
Reccomended or required readings
A. Rigamonti, P. Carretta, Structure of Matter: an Introductory Course with Problems and Solutions, Springer, 2015 (Third edition).
Assessment methods
Written and oral exams. During the course written exams dedicated to each one of the three main topics (atoms, molecules and solids) will be performed. In order to access the oral examination the student will have to pass either the three aforementioned exams or a final written exam on the three main topics. The students should try to concentrate on the common aspects used to derive the properties of atoms, molecules and solids. For example, they should be able to discuss the effects of electric fields on atoms, molecules and solids or the effects due to the exchange of indistinguishable particles in atoms, molecules and solids, or to describe the spectroscopies which can be used to determine the properties of atoms, molecules and solids.
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