  We perform an analysis of the combined effects of geometry and a magnetic
field for the case of a charged particle on a helicoid. The effective quantum
potentials for a charged spinless particle confined on a helicoid for two
simple magnetic field configurations are derived. These potentials depend
nontrivially on the surface curvature and the external magnetic field. We find
that the qualitative behavior of the effective potential can be altered by
changing the strength of the applied magnetic field. The application of a
magnetic field results in effective potentials that are either repulsive or
attractive, depending on the magnitude of the magnetic field and the angular
momentum of the particle. Finally, for the case of effective potentials that
have a minimum, we also obtain approximate expressions for the energy levels
valid when the particle is near a minimum, and these are found to be similar in
form to the energy levels of a particle in a harmonic oscillator potential.
