  The Dirichlet Laplacian between two parallel hypersurfaces in Euclidean
spaces of any dimension in the presence of a magnetic field is considered in
the limit when the distance between the hypersurfaces tends to zero. We show
that the Laplacian converges in a norm-resolvent sense to a Schroedinger
operator on the limiting hypersurface whose electromagnetic potential is
expressed in terms of principal curvatures and the projection of the ambient
vector potential to the hypersurface. As an application, we obtain an effective
approximation of bound-state energies and eigenfunctions in thin quantum
layers.
