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referframe

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## Main Question or Discussion Point

In non-relativistic QM, given a Hilbert Space with a Hermitian operator A and a generic wave function

Ψ. The operator A has an orthogonal eigenbasis, {a

I have often read that the orthogonality of such eigenfunctions is an indication of the separateness or

But what if the probability distribution for Ψ is peaked at one value causing most of the eigenvalues to be clustered in a very narrow range? How could one then say, from a

Thanks in advance

Ψ. The operator A has an orthogonal eigenbasis, {a

_{i}}.I have often read that the orthogonality of such eigenfunctions is an indication of the separateness or

*of the associated eigen***distinctiveness***i.e. that orthogonality in QM means separate and independent.***values,**But what if the probability distribution for Ψ is peaked at one value causing most of the eigenvalues to be clustered in a very narrow range? How could one then say, from a

*point-of-view, that the eigenvalues are separate or distinct, even though the eigenfunctions themselves remain orthogonal?***practical**Thanks in advance

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