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Several examples illustrate the utility of mathematical models which differ in their topological properties from the ``real'' systems they describe. The examples are the Aharonov-Bohm effect, the periodic lattice, and scattering off an obstacle. By going to the approximate topology, the Hamiltonian loses its essential self-adjointness, but the relation of the approximate to the exact topology leads to a convenient classification of its extensions.
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L. S. Schulman (1971) studied this question.
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