  We consider the Schr\"odinger operator ${\bf H}=(i\nabla+A)^2 $ in the space
$L_2({\mathbb R}^3)$ with a magnetic potential $A $ created by an infinite
straight current. We perform a spectral analysis of the operator ${\bf H}$
almost explicitly.
  In particular, 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. Equations of classical
mechanics are also integrated. Our main observation is that both quantum and
classical particles have always a preferable (depending on its charge)
direction of propagation along the current and both of them are confined in the
plane orthogonal to the current.
