Polar Gaussian State in a Two-dimensional Coulomb Potential

The Gaussian in a two-dimensional Coulomb potential has a behaviour that bears very little resemblance to a classical picture. If one uses a Gaussian spreading in polar coordinates instead, the results are more amenable to a quasi-classical interpretation. The default parameters in this simulation define a state that is concentrated around a given radius and spreads over a rather large angle. Furthermore it has a given mean angular momentum, which corresponds roughly to that of an eigenfunction that is concentrated in the same radial region.

When you start the simulation you can see mainly a rotation around the center, combined with a spreading in angular direction, until almost a whole annulus is filled up. This could vaguely be interpreted as a classical circular motion combined with a spreading caused by the uncertainty in Lz. Concentrate the "particle" in radial or angular direction and try to explain, what happens.

Measure the orbital period and compare it with the given value of Lz. Now change Lz and observe the result. Can you explain the outcome in classical terms? Can you change Lz and other parameters simultaneously to again get a rotating "particle"?