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arXiv · 1803.09313

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

Yuan You·Fa-Lin Lu·Dong-Sheng Sun·Chang-Yuan Chen·Shi-Hai Dong
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Abstract

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 axis z when the 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 spread out for b=0.5.

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Yuan You, Fa-Lin Lu, Dong-Sheng Sun, Chang-Yuan Chen, Shi-Hai Dong. 2018-03-25. The visualization of the space probability distribution for a particle moving in a double ring-shaped Coulomb potential. https://arxiv.org/abs/1803.09313

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