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Revista Mexicana de Física

Aharonov-Bohm effect on the bound states of an electron inside an annular cylindrical box

Dmitrii Kouznetsov, Eugenio Ley Koo, G. Villa‐Torres

Published Jan 1, 1999• 1 citation
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Aharonov–Bohm-type effect in the background of a distortion of a vertical line into a vertical spiral

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arXiv:1906.11000•The European Physical Journal C•Jul 1, 2019•23 citations
The Schrodinger equation for an electron inside an annular cylindrical box and in the presence of an axial uniform magnetic field is solved in two comparative situations: i) when the magnetic induction ~ B0 = kB0 is the same in the central perforation and in the box, and ii) when its values in the perforation ~ Bi = kBi and in the box ~ B0 = kB0 are different. The Aharonov-Bohm effect on the Landau states of the confined electron is exhibited through the analysis of the dependence of the energy eigenvalues and eigenfunctions on the difference of the magnetic flux in the perforation as B i i B0 changes.
It is analysed Aharonov–Bohm-type effects when a spinless quantum particle is in an elastic medium with the distortion of a vertical line into a vertical spiral. By confining the spinless particle to a cylindrical box, the analogue of the Aharonov–Bohm effect for bound states is observed due to the influence of the topological defect on the allowed energies of the system. It corresponds to the shift in the angular momentum quantum number yielded by the effects of the topology of the distortion of a vertical line into a vertical spiral. In addition, it is analysed the effects of rotation. It is shown that the Aharonov–Bohm effect for bound states exists. Besides, there is an analogue of the coupling between the angular momentum and angular velocity of the rotating frame.