Angular momentum and spin: The angular momentum operators; Eigenvalues of angular momentum operators; Angular momentum eigenfunctions; Normalization of angular momentum eigenfunctions;Spin and Spin-orbit interaction; Addition of angular momenta; Addition of two spins for the singlet and triplet eigenfunctions; Spin-orbital angular momentum addition; The Pauli exclusion principle.Approximation methods: Time independent perturbation theory; The case of a linear harmonic oscillator perturbed by an anharmonic term; The case of charged particles perturbed by static electric and magnetic fields; The variational method; JWKB approximation.
Many-particle systems: The schrodinger equation for N-particle system; Conservation of momentum; Separation of centre of mass motion; Reduced mass; Identical particles and symmetry under their interchange; Fermions and Bosons in a Box; The Fermi energy. Scattering: Collision cross section; Scattering at low energies; The Born approximation.