双环形库仑势中粒子空间几率分布的可视化
The visualization of the space probability distribution for a particle moving in a double ring-shaped Coulomb potential
摘要：
给出了双环形库仑势（RSCP）的解析解。的空间概率分布（SPD）的可视化示出的两个（轮廓）和三维（等值面）的情况下。量子数（n，l，m）主要通过双RSCP参数c与准量子数（n'，l'，m'）相关.在球坐标系中，SPD为圆环形。还讨论了相对概率值P的性质。例如，当我们考虑特殊情况（n，l，m）=（6，5，0）时，当P增加时，SPD向z轴的两极移动。最后，我们讨论了当c>0时，势参数b取正值和负值的不同情况。与特定情况b=0相比，SPD在b=-0.5时收缩，而在b=0.5时展开。
英文摘要：
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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