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In the spirit of the thin-layer quantization scheme, we give the effectiveHamiltonian describing the noninteracting electrons confined to an annularcorrugated surface, and find that the geometrically induced potential isconsiderably influenced by corrugations. By using numerical calculation, weinvestigate the eigenenergies and the corresponding eigenstates, and find thatthe transition energies can be sufficiently improved by adding corrugations.Particularly, the transition energy between the adjacent eigenstatescorresponds to energy levels difference based on the wavefunction of annularwire, and the number of the energy levels is equal to the number ofcorrugations. And the larger magnitude of corrugations is capable of increasingthe number of bound states. In addition, the distribution of ground stateprobability density is reconstructed by the corrugations, and the energy shiftis generated.

Geometric effects on the electronic structure and the bound states in annular corrugated wires