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The Aharonov-Bohm effect: Mathematical Aspects of the Quantum Flow

Dynamical Systems 2007-05-23 v1 Mathematical Physics math.MP

Abstract

This paper addresses the scattering of a beam of charged particles by an infinitely long magnetic string in the context of the hydrodynamical approach to quantum mechanics. The scattering is qualitatively analyzed by two approaches. In the first approach, the quantum flow is studied via a one-parameter family of complex potentials. In the second approach, the qualitative theory of planar differential equations is used to obtain a one-parameter family of Hamiltonian functions which determine the phase portraits of the systems.

Keywords

Cite

@article{arxiv.math/0701224,
  title  = {The Aharonov-Bohm effect: Mathematical Aspects of the Quantum Flow},
  author = {Luis Fernando Mello and Yuri Cândido Ribeiro},
  journal= {arXiv preprint arXiv:math/0701224},
  year   = {2007}
}

Comments

13 pages and 4 figures

R2 v1 2026-07-22T17:49:02.534Z