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Note that completeness of the eigenstates of a
Hermitian operator is not guaranteed, but it is extremely common for physical systems. For example, any Hermitian system whose solutions can be found with arbitrary accuracy using a sufficiently finely discretized, finite system (i.e. simulated on a
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computer) has a complete set of eigenstates, at least in the sense of generalized functions (distributions). --
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I have moved this into the article, to be dealt with there.
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