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The analytical solutions to a double ring-shaped Coulomb potential (RSCP) arepresented. The visualizations of the space probability distribution (SPD) areillustrated for the two-(contour) and three-dimensional (isosurface) cases. Thequantum 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 ringshape in spherical coordinates. The properties for the relative probabilityvalues (RPVs) P are also discussed. For example, when we consider the specialcase (n, l, m)=(6, 5, 0), the SPD moves towards two poles of axis z when the Pincreases. Finally, we discuss the different cases for the potential parameterb which is taken as negative and positive values for c>0 . Compared with theparticular case b=0 , the SPDs are shrunk for b=-0.5 while spread out forb=0.5.

The visualization of the space probability distribution for a particle moving in a double ring-shaped Coulomb potential