The code provides base functionality to calculate the wave-functions for hydrogen and visualise those wave-functions using iso-surfaces in 3D. This can be used to explore the spatial nature of the wave-functions.
In addition it is easy to calculate something approximating the wave-function of the atom whist undergoing a state transition (to make it easier to understand we assume the Rabi frequency is very slow). Then the wave-function of the atom can be visualised as a function of time whilst a transition is simulated. The transition GUI allows the user to program in any desired transition (even non-electric dipole transitions) and watch the evolution of the wave-function.

The animations clearly show why pi-transition emit linearly polarized light and sigma-transitions circular polarized light.

Developed in conjunction with Oxford Physics. Many thanks to Dr. David Lucas and Mr. Chris Ballance. The code in this submission was written by Chris Ballance whilst undertaking an internship at The MathWorks.