02-335 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 half-axis. Then we find the large-time 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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