** **

**Central force problem:** Symmetryand degeneracy, complete set of commuting observables, angular momentumconservation, Coulomb potential, 3D spherical harmonic potential

**Addition of angular momentum:** Coupled basis and uncoupled basis, Clebsch-Gordon coefficients

**Approximate methods for bound state problem:** Variational principle and variational method, time-independent perturbation theory (nondegenerate and degenerate)

**Hydrogen atom:** Fine structurecorrection (perturbative treatment), spin-orbit coupling, Diracequation (exact treatment of fine structure), beyond fine structure(Lamb shift and hyperfine correction), Hydrogen atom in external fields(Stark effect and Zeeman effect)

**Identical particles:** Quantumindistinguishability, (anti)symmetrization of many-body wavefunction,bosons and fermions, interaction between identical particles (directenergy and exchange energy)

**Multi-electron atoms and diatomic molecules:** Heliumatom (variational and perturbation calculation of ground state),multi-electron atom (central field approximation, screening effect,electronic configuration), diatomic molecules (chemical bonding,molecular potential, Born-Oppenheimer approximation, molecular energystructure)

**Time-dependent perturbation theory:** First-ordertheory, Fermi’s Golden rule, transition probability and transitionrate, sudden limit and adiabatic limit, adiabatic theorem

**Elastic scattering:** Basic concepts, Born approximation, partial wave formalism, scattering resonance, scattering between identical particles

**Atom-photon interaction:** Quantizationof electromagnetic field, electromagnetic vacuum, Wigner-Weisskopftheory of spontaneous emission, Aharonov-Bohm effect, semiclassicaltheory of atom-photon interaction, Doppler cooling of two-level atom,density matrix

**Typical Organization**

Lectures M W F 9:00 - 9:50 AM

Homework (30%) Weekly problem sets

Term exam (30%)

Final exam (40%)

Text: John S. Townsend, *A modern approach to quantum mechanics*

*All information is representative only, and is likely to change from year to year.*