The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential
Joint Authors
You, Yuan
Lu, Fa-Lin
Sun, Dong-Sheng
Chen, Chang-Yuan
Dong, Shi-Hai
Source
Advances in High Energy Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-10-08
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
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 (n, l, m) essentially related to those so-called quasi-quantum numbers (n′, l′, m′) through changing the single ring-shaped Coulomb potential parameter b.
We find that the space probability distributions (isosurface) of a moving particle for the special case l=m and the usual case l≠m are spherical and circularly ring-shaped, respectively, by considering all variables r→=(r,θ,φ) in spherical coordinates.
We also study the features of the relative probability values P of the space probability distributions.
As an illustration, by studying the special case of the quantum numbers (n, l, m) = (6, 5, 1), we notice that the space probability distribution for a moving particle will move towards the two poles of the z-axis as the relative probability value P 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 b increases.
American Psychological Association (APA)
You, Yuan& Lu, Fa-Lin& Sun, Dong-Sheng& Chen, Chang-Yuan& Dong, Shi-Hai. 2017. The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential. Advances in High Energy Physics،Vol. 2017, no. 2017, pp.1-19.
https://search.emarefa.net/detail/BIM-1122199
Modern Language Association (MLA)
You, Yuan…[et al.]. The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential. Advances in High Energy Physics No. 2017 (2017), pp.1-19.
https://search.emarefa.net/detail/BIM-1122199
American Medical Association (AMA)
You, Yuan& Lu, Fa-Lin& Sun, Dong-Sheng& Chen, Chang-Yuan& Dong, Shi-Hai. The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential. Advances in High Energy Physics. 2017. Vol. 2017, no. 2017, pp.1-19.
https://search.emarefa.net/detail/BIM-1122199
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1122199