Assuming we know all possible results of the measurements of a quantum system, that is, the set of possible eigenvalues, and suppose we also know the associated eigenfunctions, and we write the wf of the system as a linear sum of eigenfunctions each multiplied by a complex constant, is it mathematically assumed, or proven somewhere (perhaps by Von Neumann), that these eigenfunctions are orthogonal and form a basis for the Hilbert space in which they reside? TY, AG
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