On solutions of Coulomb system and its generalization to the Aharonov-Bohm effect

The paper numerically analyzes the Aharonov-Bohm effect of an infinitely thin magnetic flux for its influence on a two- or three-dimensional (3d) solutions of Coulomb system in momentum and coordinate spaces. For any definitive eigenstate, it is shown that the flux shifts the position of the most probable radius (MPR) of a probability distribution inward or outward in momentum or coordinate spaces, respectively. Moreover, the probability density of the shifted MPR is amplified in the momentum space, while reduced in the coordinate space. Since the Coulomb force among charged particles dominate the structure of matter, shifting of the MPR controlling by the flux effect may be beneficial to the construction of nanostructure by manipulating the atomic and molecular bonds.