The Visualization of the Space Probability Distribution for a Particle Moving in a Double Ring-Shaped Coulomb Potential

Abstract EN

The analytical solutions to a double ring-shaped Coulomb potential (RSCP) are presented.

The visualizations of the space probability distribution (SPD) are illustrated for the two- (contour) and three-dimensional (isosurface) cases.

The quantum numbers (n,l,m) are mainly relevant for those quasi-quantum numbers (n′,l′,m′) via the double RSCP parameter c.

The SPDs are of circular ring shape in spherical coordinates.

The properties for the relative probability values (RPVs) P are also discussed.

For example, when we consider the special case (n,l,m)=(6,5,0), the SPD moves towards two poles of z-axis when P increases.

Finally, we discuss the different cases for the potential parameter b, which is taken as negative and positive values for c>0.

Compared with the particular case b=0, the SPDs are shrunk for b=-0.5, while they are spread out for b=0.5.