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The visualization of the space probability distribution for a particle moving in a double ring-shaped Coulomb potential
Yuan You, Fa-Lin Lu, Dong-Sheng Sun +2
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-…
The visualization of the space probability distribution for a moving particle I: in a single ring-shaped Coulomb potential
Yuan You, Fa-Lin Lu, Dong-Sheng Sun +2
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 wit…
Ring-shaped potential and a class of relevant integrals involved universal associated Legendre polynomials with complicated arguments
Wei Li, Chang-Yuan Chen, Shi-Hai Dong
We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. Its generating function is applied to obtain a…
Legitimacy of wave-function expansion
Changye Chen
In this letter we investigate the common procedure in which any wave function is expanded into a series of eigenfunctions. It is shown that as far as dynamical systems are concerne…