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**Ket Notation -- Effects of the Projection Operator**

## Homework Statement

From Sakurai's Modern Quantum Mechanics (Revised Edition), it is just deriving equation 1.3.12.

## Homework Equations

[tex] \begin{eqnarray*}\langle \alpha |\cdot (\sum_{a'}^N |a'\rangle \langle a'|) \cdot|\alpha \rangle \end{eqnarray*} [/tex]

## The Attempt at a Solution

The summation can be moved to the left, so everything is being summed from a' to N, but does an alpha bra inner product with a' (or <α|a'>) does the sum of this from all a' to N equal Ʃ<a'|α>? maybe this is simple and I just can't see it?