• A Particle in a Central Field

  • The asymptotic behavior of the radial functions, two interacting particles.

• Hydrogenic Systems

  • The hydrogen atom, eigenvalues and eigenfunctions, spectroscopic notation, hydrogenic systems.

• Diatomic Molecules

  • Motion of the nuclei, vibrational-rotational levels.

• Addition of Angular Momentum

  • Clebsch-Gordan coefficients, adding more than two angular momenta, rotation matrices, transformation properties of the spherical harmonics, the Wigner-Eckart theorem, the projection theorem.

• Gauge Transformations, Flux Quantization, Propagator

  • Gauge transformations in electromagnetism, the Aharonov-Bohm effect, magnetic monopoles, propagator and path integrals.

• Periodic Systems

  • Periodic and continuous systems, Electrons in a solid.

• Scattering

  • Scattering by a central potential, free spherical waves, partial waves, phase shifts,   the scattering cross section near a resonance, scattering length and effective range, frame transformations, integral scattering equation for stationary states, the Born approximation, the Yukawa potential, the Coulomb potential.

• Approximation Methods for bound states

  • Stationary perturbation theory, the perturbation of degenerate states, the variational method,

• The fine structure and hyperfine structure of H

  • The Dirac equation, the fine structure Hamiltonian, the hyperfine structure Hamiltonian.

• Time Dependent Perturbation Theory

  • Atoms interacting with an electromagnetic wave, transition selection rules

• Identical Particles

  • Permutation operators, Slater Determinants, atomic spectra, coupling schemes