The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential
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) visu...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/7937980 |
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| author | Yuan You Fa-Lin Lu Dong-Sheng Sun Chang-Yuan Chen Shi-Hai Dong |
| author_facet | Yuan You Fa-Lin Lu Dong-Sheng Sun Chang-Yuan Chen Shi-Hai Dong |
| author_sort | Yuan You |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f17f876a599f4575abc9e15212c1f1c1 |
| institution | Kabale University |
| issn | 1687-7357 1687-7365 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in High Energy Physics |
| spelling | doaj-art-f17f876a599f4575abc9e15212c1f1c12025-02-03T01:06:59ZengWileyAdvances in High Energy Physics1687-73571687-73652017-01-01201710.1155/2017/79379807937980The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb PotentialYuan You0Fa-Lin Lu1Dong-Sheng Sun2Chang-Yuan Chen3Shi-Hai Dong4New Energy and Electronic Engineering, Yancheng Teachers University, Yancheng 224002, ChinaNew Energy and Electronic Engineering, Yancheng Teachers University, Yancheng 224002, ChinaNew Energy and Electronic Engineering, Yancheng Teachers University, Yancheng 224002, ChinaNew Energy and Electronic Engineering, Yancheng Teachers University, Yancheng 224002, ChinaLaboratorio de Información Cuántica, CIDETEC, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, 07700 Ciudad de México, MexicoWe 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.http://dx.doi.org/10.1155/2017/7937980 |
| spellingShingle | Yuan You Fa-Lin Lu Dong-Sheng Sun Chang-Yuan Chen Shi-Hai Dong The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential Advances in High Energy Physics |
| title | The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential |
| title_full | The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential |
| title_fullStr | The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential |
| title_full_unstemmed | The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential |
| title_short | The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential |
| title_sort | visualization of the space probability distribution for a moving particle in a single ring shaped coulomb potential |
| url | http://dx.doi.org/10.1155/2017/7937980 |
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