Dirac ket-bra simplification over here.

[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.

 

[unxviper]

Using the orthogonality condition

 

[Bill_K]

Along with U^†U = I.

 

[M. next]

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

 

[M. next]

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

 

[kith]

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

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

 

[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?

 

[kith]

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