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arXiv:1103.1607 · Quantum Information Processing

Quantum measurement and the Aharonov–Bohm effect with superposed magnetic fluxes

Kaća Bradonjić, John D. Swain

Published Oct 16, 2013• 2 citations
arXivHTMLPDF
DOI
10.1007/s11128-013-0652-3

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In this work, we solve the radial Schrödinger wave equation in three dimensions under Aharonov–Bohm (AB)-flux field with potential superposition of generalized q-deformed Hulthen potential, Coulomb potential, and inverse quadratic Yukawa potential in a point-like defect. We determine the approximate eigenvalue solution using the parametric Nikiforov–Uvarov (NU) method and analyze the effects of topological defect and the magnetic flux field with this superposed potential. We show an analogous of the AB effect because the eigenvalue solution depends on the geometric quantum phase and bound state solutions are possible under condition. Finally, we utilize the approximate eigenvalue solution to some molecular potential models, such as Deng–Fan potential and inverse quadratic Hulthen potential and analyze the effects on the energy levels and the radial wave functions.
A useful and universal formula for the expectation value of the radial operator in the presence of the Aharonov-Bohm flux and the Coulomb Field is established. We find that the expectation value <rλ>< r^λ><rλ> (−∞≤λ≤∞)(-\infty \leq λ\leq \infty)(−∞≤λ≤∞) is greatly affected due to the non-local effect of the magnetic flux although the Aharonov-Bohm flux does not have any dynamical significance in classical mechanics. In particular, the quantum fluctuation increases in the presence of the magnetic flux due to the Aharonov-Bohm effect. In addition, the Virial theory in quantum mechanics is also constructed for the spherically symmetric system under the Aharonov-Bohm effect.