Prove that eigenstates of hermitian operator form a complete set

[fa2209]

Not really sure how to go about this. Our lecture said "it can be shown" but didn't go into any detail as apparently the proof is quite long. I'd really appreciate it if someone could show me how this is done. Thanks. (Not sure if this is relevant but I have not yet studied Hilbert spaces).

 

[dextercioby]

The proof is complicated and it appears in dozens of books on functional analysis. If you're not acquainted to HS and measure theory, then it basically makes little sense to read it.

 

[arkajad]

Not really sure how to go about this. Our lecture said "it can be shown" but didn't go into any detail as apparently the proof is quite long. I'd really appreciate it if someone could show me how this is done. Thanks. (Not sure if this is relevant but I have not yet studied Hilbert spaces).

Can you prove that a hermitian operator has at least one eigenvector? You should really start with this property.