Quantum Structure of Matter

1. Introductory theory: Brief review of the basics of quantum mechanics. The hydrogen atom: eigenvalues, eigenstates, s- and p-orbitals. Basic theory of spin, identical particles. Perturbation theory and variational methods. (duration: 2 weeks).
2. Atoms:The notion of the effective central potential. Lifting of the hydrogen-like degeneracy. The periodic system of elements. Simple order of magnitude estimates. Approximate calculation of the ground state of the Helium atom. The real hydrogen atom. Fine and hyperfine structure. The states of multi-electron systems. Hund’s rules.(duration: 4 weeks)
3. Molecules: Introduction to the concept of the chemical bond. The double well. Structure and properties of a few simple molecules (H2, O2, H2O, NH3). Detailed study of the ammonia molecule. The ammonia maser.Orbital hybridization of chemical bonds and carbon compounds. Delocalized chemical bonds. The many well system in linear or cyclic arrangements. Conjugated and aromatic hydrocarbons (polyacetylene and benzene). A quantitative calculation from first principles: the molecular hydrogen ion.(duration: 3 weeks)
4. Solids: The one-dimensional solid and the tight-binding approximation (linear combination of atomic orbitals). Energy bands and the problem of electrical conductivity. Conductors, semiconductors and insulators. Fermi energy and the density of states. Ultradense matter and the Chandrasekhar limit.(duration 2 weeks)
5. Matter and light. Phenomenology of the interaction of light with atoms. The concepts of rate, cross-section and mean-free-path. The Fermi rule and its application to the process of resonance. Laser light and its properties. Polarized photons and polarizers.(duration 2 weeks)