  In the spirit of the thin-layer quantization scheme, we give the effective
Hamiltonian describing the noninteracting electrons confined to an annular
corrugated surface, and find that the geometrically induced potential is
considerably influenced by corrugations. By using numerical calculation, we
investigate the eigenenergies and the corresponding eigenstates, and find that
the transition energies can be sufficiently improved by adding corrugations.
Particularly, the transition energy between the adjacent eigenstates
corresponds to energy levels difference based on the wavefunction of annular
wire, and the number of the energy levels is equal to the number of
corrugations. And the larger magnitude of corrugations is capable of increasing
the number of bound states. In addition, the distribution of ground state
probability density is reconstructed by the corrugations, and the energy shift
is generated.
