Is it possible to show that an ONB (orthonormal base is complete). I am quite irritated by the insertions of ones of the form [tex]\sum_{n} \left| \Psi_n \right\rangle \left\langle \Psi_n\right|[/tex] if the vectors are the eigenvectors of some Hamiltonian. So now the more precise questions:(adsbygoogle = window.adsbygoogle || []).push({});

1) Is there a straight forward approach to show that an ONB is complete in the Schwarz space, C2 or rigged Hilbert space.

2) If this is a property of Hermitian operators what are the restrictions? (the base formed by eigenfunctions of a finite potential well for example is obviously over complete)

3) If it is not straight forward: Let's say we have a well known ONB like the eigenfunctions of the harmonic oscillator. Then we take away the eigenfunction for one quantum number like n=5. How is it possible to show that this base is incomplete without the explicit use of that function?

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# Show that an ONB is complete

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