Gaussian Wave Packet in a Two-dimensional Coulomb Potential

For the harmonic oscillator the Gaussian wave function has a lot of interesting properties, but for the two-dimensional Coulomb potential it is not very illuminative: Starting the applet with its default values shows a very complicated and seemingly chaotic behaviour.

Looking more closely one finds features that reveal connections between the classical and quantum description of the system:

Another interesting phenomenon is the decrease of the total probability P with time, which reaches a steady value < 1 after some time. Study this decrease for different values of s and v0. Can you find a qualitative explanation of your findings?