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

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

2007-01-08

arxiv.org/abs/math/0701224v1

Mathematics

Dynamical Systems

13 pages and 4 figures

Scientific paper

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.

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