Dirac ket-bra simplification over here.

1. Apr 5, 2014

M. next

I usually know how to manipulate bras and kets. But I probably found difficulty because of the double summation. How did Sakurai manage to go from the second line to the ird line in the attachment?

SECTION 4.4 in Sakurai.

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2. Apr 5, 2014

unxviper

Using the orthogonality condition

Last edited: Apr 5, 2014
3. Apr 5, 2014

Bill_K

Along with UU = I.

4. Apr 6, 2014

M. next

How come? If so I will end up with a zero, no?

5. Apr 6, 2014

M. next

I was thinking about taking duality but that didn't seem to work.

6. Apr 6, 2014

kith

No. What is $\langle a''|a' \rangle$ equal to and what does this imply for $\Sigma_{a''} \langle a''|a' \rangle$?

7. Apr 6, 2014

M. next

It is equal to 1 if a=a'' and 0 otherwise if we take orthogonality into consideration.. It implies that the summation = 1 when a'' = a' and 0 for all the other summations. Right?

8. Apr 6, 2014

kith

Yes. If you put Bill's comment and this together, do you still miss something to go from line two to line three?