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Advances in High Energy Physics
Volume 2017 (2017), Article ID 7937980, 19 pages
Research Article

The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential

1New Energy and Electronic Engineering, Yancheng Teachers University, Yancheng 224002, China
2Laboratorio de Información Cuántica, CIDETEC, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, 07700 Ciudad de México, Mexico

Correspondence should be addressed to Yuan You; moc.361@w_uoynauy, Chang-Yuan Chen; ten.361@yccctcy, and Shi-Hai Dong; moc.oohay@2hsgnod

Received 4 March 2017; Accepted 9 April 2017; Published 8 October 2017

Academic Editor: Saber Zarrinkamar

Copyright © 2017 Yuan You et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


We first present the exact solutions of the single ring-shaped Coulomb potential and then realize the visualizations of the space probability distribution for a moving particle within the framework of this potential. We illustrate the two-dimensional (contour) and three-dimensional (isosurface) visualizations for those specifically given quantum numbers (, , ) essentially related to those so-called quasi-quantum numbers (, , ) through changing the single ring-shaped Coulomb potential parameter . We find that the space probability distributions (isosurface) of a moving particle for the special case and the usual case are spherical and circularly ring-shaped, respectively, by considering all variables in spherical coordinates. We also study the features of the relative probability values of the space probability distributions. As an illustration, by studying the special case of the quantum numbers (, , ) = (6, 5, 1), we notice that the space probability distribution for a moving particle will move towards the two poles of the -axis as the relative probability value increases. Moreover, we discuss the series expansion of the deformed spherical harmonics through the orthogonal and complete spherical harmonics and find that the principal component decreases gradually and other components will increase as the potential parameter increases.