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Using a momentum representation of a magnetic von Neumann lattice, we study atwo-dimensional electron in a uniform magnetic field and obtain one-particlespectra of various periodic short-range potential problems in the lowest Landaulevel.We find that the energy spectra satisfy a duality relation between aperiod of the potential and a magnetic length. The energy spectra consist ofthe Hofstadter-type bands and flat bands. We also study the connection betweena periodic short-range potential problem and a tight-binding model.Comment: 6 pages, 3 figures, final version to appear in PR

Duality relation among periodic-potential problems in the lowest Landau level