The Aharonov–Bohm effect in the momentum space

Dragoman, Daniela; Богдан, Стефан

doi:10.1016/j.optcom.2007.12.090

Cited by 2 publications

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“…However, the relations between different approaches, and different contexts in which the effect appears are not completely understood (see review in [8]), the behavior of phase for non-cyclic evolutions is barely discussed, and the case of n ≥ 2 parallel coils is not yet solved [11,12]. We also note that the analysis of the problem in the momentum representation, apart from few exceptions [11,13,14] is almost absent as opposed to coordinate representation.…”

Section: Introductionmentioning

confidence: 99%

On the scattering Aharonov–Bohm effect

Ivetić

2019

Phys. Scr.

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In this paper we review some aspects of the scattering Aharonov-Bohm effect and Berry's phase. Specifically, the problem of scattering of free 2d electrons on the system of an arbitrary number of parallel, infinitely thin and infinitely long coils (non-interacting, point magnetic fluxes) is modeled as free semi-classical particle propagation on a topologically nontrivial background. We show that in this case it is possible to obtain Berry's phase by integration. First the case of a single coil is analyzed, upon which a particular solution for the case of scattering on an arbitrary number of coils is found. Considering the solution in the momentum representation, an analytic continuation of the angle coordinate in the momentum space is introduced, in accord with the nontrivial geometry of the configuration space. Finally, some simple experiments with possible applications for quantum computing are proposed. * bivetic@yahoo.com

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Section: Introductionmentioning

confidence: 99%

On the scattering Aharonov–Bohm effect

Ivetić

2019

Phys. Scr.

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“…Actually, starting with Dirac equation [13][14][15][16][17][18] both sAB and AC effects have been investigated separately. After writing Dirac Lagrangian [19][20][21][22][23][24][25][26] and Hamiltonian [27][28][29][30][31] the above-mentioned Schrödinger equation can be expressed. In nonrelativistic limit, an effective Lagrangian can describe the interaction between charged particle and a magnetic moment.…”

Section: Introductionmentioning

confidence: 99%

Biquaternionic Description of the Schrödinger Equation

Tanışlı

Demir

2012

MCA

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This paper begins with the introduction of biquaternion algebra and its properties in compact, profound and comprehensible approach. The Schrödinger equation including both the scalar Aharonov-Bohm(sAB) and Aharonov-Casher(AC) effects, that are currently popular in particle physics and condensed-matter physics, has been rewritten by biquaternions. The newly biquaternionic Schrödinger equation, which is defined with various assumptions and approaches, also includes the biquaternionic generalized momentum in Hamiltonian.

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The Aharonov–Bohm effect in the momentum space

Abstract: ABSTRACT:The Schrödinger formalism of quantum mechanics is used to demonstrate the existence of the Aharonov-Bohm effect in momentum space and set-ups for experimentally demonstrating it are proposed for either free or ballistic electrons.

Cited by 2 publications

References 15 publications

On the scattering Aharonov–Bohm effect

On the scattering Aharonov–Bohm effect

Biquaternionic Description of the Schrödinger Equation

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