  Quantum mechanics of bending of a nonrelativistic monoenergetic charged
particle beam by a dipole magnet is studied in the paraxial approximation. The
transfer map for the position and momentum components of a particle of the beam
between two transverse planes at different points on the curved optic axis of
the system is derived starting with the nonrelativistic Schr\"{o}dinger
equation. It is found that the quantum transfer map contains the classical
transfer map as the main part and there are tiny quantum correction terms. The
negligibly small quantum corrections explain the remarkable success of
classical mechanics in charged particle beam optics.
