In two dimensions the microscopic theory, which provides a basis for the
naive analogy between a quantized vortex in a superfluid and an electron in an
uniform magnetic field, is presented. A one-to-one correspondence between the
rotational states of a vortex in a cylinder and the cyclotron states of an
electron in the central gauge is found. Like the Landau levels of an electron,
the energy levels of a vortex are highly degenerate. However, the gap between
two adjacent energy levels does not only depend on the quantized circulation,
but also increases with the energy, and scales with the size of the vortex.Comment: LaTeX, 4 pages, 2 EPS figures, To appear in ``Series on Advances in
Quantum Many-Body Theory'' ed. by R.F. Bishop, C.E. Campbell, J.W. Clark and
S. Fantoni (World Scientific, 2000
