  Every energy level of a charged quantum particle confined in a region
threaded by a magnetic flux line with quantum flux one-half must be degenerate
for some position of the semifluxon within the boundary B. This is illustrated
by computations for which B is a circle and a conformal transformation of a
circle without symmetry. As the shape of B is varied, two degeneracies between
the same pair of levels can collide and annihilate. Degeneracy of three levels
requires three shape parameters, or the positions of three semifluxons;
degeneracy of N levels can be generated by int{N(N+1)/4} semifluxons. The force
on the semifluxon is derived.
