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The detailed study of a quantum free particle on a pointed plane isperformed. It is shown that there is no problem with a mysterious ``quantumanticentrifugal force" acting on a free particle on a plane discussed in a veryrecent paper: M. A. Cirone et al, Phys. Rev. A 65, 022101 (2002), but we dealwith a purely topological efect related to distinguishing a point on a plane.The new results are introduced concerning self-adjoint extensions of operatorsdescribing the free particle on a pointed plane as well as the role played bydiscrete symmetries in the analysis of such extensions.Comment: 4 figure

Quantum mechanics of a free particle on a plane with an extracted point