  We study the motion of a charged quantum particle, constrained on the surface
of a cylinder, in the presence of a radial magnetic field. When the spin of the
particle is neglected, the system essentially reduces to an infinite family of
simple harmonic oscillators, equally spaced along the axis of the cylinder.
Interestingly enough, it can be used as a quantum Fourier transformer, with
convenient visual output. When the spin 1/2 of the particle is taken into
account, a non-conventional perturbative analysis results in a recursive closed
form for the corrections to the energy and the wavefunction, for all
eigenstates, to all orders in the magnetic moment of the particle. A simple
two-state system is also presented, the time evolution of which involves an
approximate precession of the spin perpendicularly to the magnetic field. A
number of plots highlight the findings while several three-dimensional
animations have been made available on the web.
