- #1

dingo_d

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## Homework Statement

In the proof that two observables [tex]\hat{O}[/tex] and [tex]\hat{O}'[/tex] commute iff they admit a common basis of eigenvectors, I'm not understanding one part.

## Homework Equations

If [tex]{|a_k\rangle}[/tex] is basis in Hilbert space we have:

[tex](OO')_{jk}=\langle a_j|\hat{O}\hat{O}'|a_k\rangle=\sum_n\langle a_j|\hat{O}|a_n\rangle\langle a_n|\hat{O}'|a_k\rangle=\sum_n\hat{O}_{kn}\hat{O}'_{nj}[/tex]

Now I'm confused a bit. And maybe I'm not understanding the matter that well (I'm only starting to study QM), but why is the last part

[tex]\sum_n\hat{O}_{kn}\hat{O}'_{nj}[/tex] and not [tex]\sum_n\hat{O}_{jn}\hat{O}'_{nk}[/tex]?

I mean it 'feels' to me that the latter should be true, because it is in the brackets (I mean the indices)...