FUNDAMENTALS OF MODERN PHYSICS

1) Solution of the Schroedinger equation for a system of two particles in a central potential. Spherica harmonics and radial solution. Relevant expectation values. Virial theorem for a one-electron atom.
2) Time independent perturbation theory (non degenerate and degenerate case). Examples. Time-dependent perturbation theory: perturbation switched on at to and then constant, periodic perturbation. Rabi frequency.
3) Interaction of one-electron atom with an electromagnetic field. Transition rate, dipole approximation, cross section for stimulate absorption/emission. Spontaneous emission. Selection rules for one-electron atoms. Spin of photons: Beth experiment. Sum rule.
4) Lifetime of an electronic state. Line shape: pressure and Doppler broadening. Examples. Laser, maser. Ammonia maser, solid-state laser. Modern spectroscopies: examples of sub-Doppler spectroscopies.
5) Photoelectric effect: cross section for one-electron atom in 1s state. Comparison with experimental data.
6) Scattering: differential cross section for elastic and inelastic (Rayleigh and Thomson) scattering. Partial waves and corresponding cross section calculation.
7) Composition of angular momenta. Fine structure of one-electron atoms: spin-orbit, Darwin and relativistic terms. Calculation of some electronic energy levels for on-electron atoms. Lamb shift. Elements of hyperfine structure. 21-cm transition of H.
8) Zeeman effect: normal (examples, observed transitions and polarization, Paschen-Bach case), anomalous, case of ultra strong magnetic fields.
9) Stark-Lo Surdo effect for one-electron atoms: linear (n=1, n=2) and quadratic (n=2). Atomic static polarizability. Quenching of the 2s state of hydrogen. Ionization indiced by an electric field.
10) Many-electron atoms. Triplet and singlet states. Pauli exclusion principle (strong and weak conditions). Helium atom (independent electron model, nuclear effective charge). Ground state for a two-electron atom: first order perturbation. Pure discrete excited states, Auger effect. Variational method and application to for the ground state of a two-electron atom.
11) Central potential for a two-electron atom. Hartree theory and results. Slater determinant. Note on the Hartree-Fock method. Results, periodic table of the elements.
12) Correction to the central field: L-S coupling (examples of electronic configuration, degeneracy.). j-j coupling.
13) Molecules: Born-Oppenheimer approximation. Schroedinger solution of H2+ molecule by linear combination of atomic orbitals and of H2. Vibrational and rotational dynamics.
14) Quantum statistics, occupation index: Bose-Einstein and Fermi-Dirac cases with examples.