  We study the motion of a particle in a particular magnetic field
configuration both classically and quantum mechanically. For flux-free radially
symmetric magnetic fields defined on circular regions, we establish that
particle escape speeds depend, classically, on a gauge-fixed magnetic vector
potential, and demonstrate some trajectories associated with this special type
of magnetic field. Then we show that some of the geometric features of the
classical trajectory (perpendicular exit from the field region, trapped and
escape behavior) are reproduced quantum mechanically using a numerical method
that extends the norm-preserving Crank-Nicolson method to problems involving
magnetic fields. While there are similarities between the classical trajectory
and the position expectation value of the quantum mechanical solution, there
are also differences, and we demonstrate some of these.
