Addition of Angular Momenta:

Total angular momentum in classical mechanics, total angular momentum in quantum mechanics, addition of two spin  ½  angular  momenta,  addition  of  two  arbitrary  angular  momenta, Clebsch-Gordon coefficients, sddition of spherical harmonics, vector operators, Wigner-Eckart theorem, electric Multi-pole moments, Evolution of two angular momenta J1 and J2 coupled by an interaction aJ1 . J2.

Stationary Perturbation Theory:

Description of the method, perturbation of a non-degenerate level, perturbation of a degenerate level, one-dimensional harmonic oscillator subjected to a perturbing potential, interaction between the magnetic dipoles of two spin ½ particles, Van der waals forces, volume effect and The influence of the spatial extension of the nucleus on the atomic levels, variational method, energy bands of electrons in solids, a  simple example of the chemical bond: The  ion

Applications of Perturbation Theory to Atomic Systems:

Fine and hyperfine structure of atomic levels in hydrogen,   Calculation of the mean values  of  the  spin-orbit coupling  in  the  1s,  2s  and  2p  levels,  hyperfine structure And the Zeeman effect for muonium and positronium, Stark effect .

Approximation Methods for Time-Dependent Problems:

Statement of the problem, approximate solution of the Schrodinger equation, An important special case: Sinusoidal or constant perturbation, Interaction of an atom with electromagnetic waves, linear and non-linear response of a two-level system subjected to a sinusoidal perturbation, Ooscillations of a system between two discrete states under the effect of a resonant perturbation, Rabi flopping, decay of discrete state resonantly coupled to a continuum of final states, Fermi’s golden rule

Systems of Identical Particles:

Identical particles, Permutation operators, The symmetrization postulate, difference between bosons and fermions, Pauli’s exclusion principle, many-electrons atom and their electronic configurations, energy levels of the helium atom, configurations, terms, multiplets, spin isomers of hydrogen (ortho and parahydrogen)

Scattering by a Potential:

Importance of collision phenomena, Stationary scattering states, scattering cross section, scattering by a central potential, method  of  partial  waves,  phenomenological description of  collisions  with absorption.