PHYS598MAP Spring 2005 Blog

1. Hydrogen wavefunctions are products of a radial wavefunction and spherical harmonics. The wavefunction is completely specified by quantum numbers n,l,m, and the energy only depends on n. Only s-states have non-zero amplitude at the origin.
   note: It does look like those 3-d images of the hydrogen wavefunctions are OK. The phase variation outside of the f coordinate is binary, and just represents sign changes.

2. The fine-structure in an atom is due to relativistic corrections to the electronic wavefunction. There are three parts to fine structure: kinetic energy corrections, spin-orbit interaction, and the mysterious Darwin term. It's difficult to make sense of these terms without using the Dirac equation. The fine-structure Hamiltonian is diagonal with respect to the total angular momentum J, and, with fine-structure present, the energy of the atomic states depends on the quantum numbers n and j.

3. The degeneracy between Hydrogenic states with the same n and j is lifted by the Lamb shift (known as a radiative correction), which is a pure QED effect. The first measurement of the Lamb shift prompted the development of QED; current measurements are getting to the level where the effect of the proton charge distribution can be resolved. A (mostly) incorrect model from Welton can be used to conceptually understand the Lamb shift and estimate the splitting between the Hydrogen 2s_1/2 and 2p_1/2 states to within an order of magnitude.

See you Tuesday! Definitely bring a calculator; we will be calculating fine and hyperfine structure for the alkali atoms.

Brian