TY - JOUR
T1 - The Visualization of the Space Probability Distribution for a Moving Particle
T2 - In a Single Ring-Shaped Coulomb Potential
AU - You, Yuan
AU - Lu, Fa Lin
AU - Sun, Dong Sheng
AU - Chen, Chang Yuan
AU - Dong, Shi Hai
N1 - Publisher Copyright:
© 2017 Yuan You et al.
PY - 2017
Y1 - 2017
N2 - 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,) 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.
AB - 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,) 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.
UR - http://www.scopus.com/inward/record.url?scp=85042084698&partnerID=8YFLogxK
U2 - 10.1155/2017/7937980
DO - 10.1155/2017/7937980
M3 - Artículo
SN - 1687-7357
VL - 2017
JO - Advances in High Energy Physics
JF - Advances in High Energy Physics
M1 - 7937980
ER -