Abstract
The energy spectrum of an electron confined to a mesoscopic surface of revolution in an external magnetic field, parallel to the symmetry axis, is studied analytically. Via conformal mapping the problem is reduced to the problem on the surface of a sphere. Cases of the sphere and the spheroid are considered in detail and the dependence on parameters is discussed. In the high magnetic field limit we observe a Landau level-like regular structure of the electron energy spectrum.
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