 02335 Yafaev D.
 A particle in a magnetic field of an infinite rectilinear current
(32K, LATeX 209)
Jul 30, 02

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Abstract. We consider the Schr\"odinger operator ${\bf H}=(i\nabla+A)^2 $ in the
space $L_2({\R}^3)$ with a magnetic
$A $ potential created by an infinite rectilinear current.
We show that the operator ${\bf H}$ is absolutely continuous, its spectrum
has infinite
multiplicity
and coincides with the positive halfaxis. Then we find the largetime
behavior of solutions
$\exp(i{\bf H}t)f$ of the time dependent Schr\"odinger equation. Our main
observation is that
a quantum particle has always a preferable (depending on its charge)
direction of propagation along the current. Similar result is true in
classical mechanics.
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02335.tex