List of Modules

Syllabus List of Modules Schedule Discussion

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

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