  The detailed study of a quantum free particle on a pointed plane is
performed. It is shown that there is no problem with a mysterious ``quantum
anticentrifugal force" acting on a free particle on a plane discussed in a very
recent paper: M. A. Cirone et al, Phys. Rev. A 65, 022101 (2002), but we deal
with a purely topological efect related to distinguishing a point on a plane.
The new results are introduced concerning self-adjoint extensions of operators
describing the free particle on a pointed plane as well as the role played by
discrete symmetries in the analysis of such extensions.
