Bound Electron States on a Curved Surface

We examine electrons bound in quantum-mechanical states in the surface region of a cylindrically curved surface. As predicted by Prange, the energy-level scheme for such states is formally identical with that of a flat-surface sample, except for the replacement of magnetic field H by an effective field Heff=H(1+RcRₛ), where Rc and Rₛ are the cyclotron and surface-curvature radii, respectively. The predicted field shift of the microwave impedance-oscillation spectrum of a (100)-plane Cu sample in weak magnetic fields has been observed and measured; this has allowed us to determine both the curvature radius K and the Fermi velocity vF at the [100] point of the Cu Fermi surface. We find K=0.36×10⁸ cm^-1 and vF=1.11×10⁸ cm/sec.