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 computer) has a complete set of eigenstates, at least in the sense of generalized functions (distributions). -- Steven G. Johnson

I have moved this into the article, to be dealt with there. The Anome