a little while …

some plots from my thesis. it is a pictorial representation of transition rates of electrons bound by a two dimensional image potential (i.e. particle-in-a-box) on a metal surface as a function of the polar and azimuthal angles relative to the vertical axis. these electrons are excited first to their image potential state by a photon, let’s say, and from there are knocked again with a light ray to eject them into the vacuum. i have no idea if the mathematics are correct, but nonetheless, i get pretty neat looking plots, which sort of correlate with some of my expectations.

Here is Fermi’s Golden Rule:

in english, the dimensions are NUMBER/TIME, where number is the number of transitions from an initial state, i, to a final state, f.

Here are some plots for several initial states at a square potential size comparable to the bohr radius. the final state is always the same, the continuum state, which is an electron completely liberated from the image potential traveling happily through the vacuum.

this is the ground state, and i kinda expected it to look like this … not sure why there are nodes though.