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Universe

Bound States for the Spin-1/2 Aharonov-Bohm Problem in a Rotating Frame

Daniel F. Lima, Márcio M. Cunha, Luís Fernando C. Pereira, Edilberto Oliveira Silva

Published Nov 23, 2021• 2 citations
Publisher

Abstract

In this paper, we study the effects of rotation in the spin-1/2 non-relativistic Aharonov-Bohm problem for bound states. We use a technique based on the self-adjoint extension method and determine an expression for the energies of the bound states. The inclusion of the spin element in the Hamiltonian guarantees the existence of bound state solutions. We perform a numerical analysis of the energies and verify that both rotation and the spin degree of freedom affect the energies of the particle. The main effect we observe in this analysis is a cutoff value manifested in the Aharonov-Bohm flux parameter that delimits the values for the positive and negative energies.

DOI
10.3390/universe7120457

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In this paper, we study the effects of rotation in the spin-1/2 non-relativistic Aharonov-Bohm problem for bound states. We use a technique based on the self-adjoint extension method and determine an expression for the energies of the bound states. The inclusion of the spin element in the Hamiltonian guarantees the existence of bound state solutions. We perform a numerical analysis of the energies and verify that both rotation and the spin degree of freedom affect the energies of the particle. The main effect we observe in this analysis is a cutoff value manifested in the Aharonov-Bohm flux parameter that delimits the values for the positive and negative energies.
Universal critical ggg factor for spin-1/2 Aharonov-Bohm bound states
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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.