QM II topics covered
Barrier penetration, potential scattering, Born approximation. Differential and total cross sections. Partial waves, phase shifts. Argand diagrams and Breit-Wigner resonances. The optical theorem. The S-matrix. Time dependent Schrödinger equation. Fermi's Golden Rule. Radiative transitions. Path Integrals. Group theory in QM.

Class notes (pdf)
QM II topics 1D scattering amplitudes figs 3D scattering: general aspects; Born series. Born approx e.g.s of diff and total cross sections; radial potentials, Coulomb and screened Coulomb. Partial wave analysis, phase shifts; relation to cross section. Intuition for phase shifts; hard sphere phase shifts, partial and total cross sections; exact and Born-order phase shift integrals. Argand diagrams and Breit-Wigner phase shifts. The optical theorem. The S-matrix. An aside on momentum space wfns, bases, and abstract state vectors. Review material for midterm. Time dependent Schrödinger equation. Choice of picture. Time dependent perturbation theory. Fermi's Golden Rule. E1 transition rate formulas for all allowed H transitions to Ni=6. Radiative transitions. Derivation of the E1 decay rate formula. Notes on vector spherical harmonics {Yjlm}: properties; examples. Path Integrals: Definitions. Consistency with the Schrödinger equation. PI2: An explicit example. Eigenmode expansions. Relation to QM operators. Group Theory and QM 1: Basic properties of groups. GT2: Representation theory. An example of applying group theory to physics: analysis of an S3 symmetric Hamiltonian. GT3: Young tableaux, basis vectors, irreducible representations of Sn. GT4: Continuous groups, Lie groups and Lie algebras. The origin of SU(n) symmetry in physics. Global and local gauge theories. GT5: Irreps of continuous groups and their basis vectors; SU(2), SU(3), SU(n). Color SU(3), isospin SU(2) and flavor SU(3). Quark model states. QM at finite temperature. Boltzmann distribution, thermal averages. Density matrices and trace formulas. High temperature series. Identical particles; independent states. Spin-statistics theorem. Symmetrization and antisymmetrization of many-body wavefunctions. Rotations using Euler angles. Rotation matrices. Wigner d-functions. Products of rotation matrices. Gaunt formula redux. Rigid rotator in QM. Review material for final.