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In the 3rd edition, on page 118, the projection operator is introduced as

$$\hat{P}=|\alpha\rangle\langle\alpha|.$$

Then Griffiths says that when $\hat{P}$ acts on another vector, it looks like this:

$$\hat{P}|\beta\rangle=(\langle\alpha|\beta\rangle)|\alpha\rangle.$$

I'm having trouble understanding why it looks like above and not like this:

$$\hat{P}|\beta\rangle=|\alpha\rangle(\langle\alpha|\beta\rangle).$$

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    $\begingroup$ It's the same. It's just multiplication of a vector by a number. $\endgroup$ – Javier Apr 21 at 5:00
  • $\begingroup$ Oh right, the inner product is just a number. Thanks! $\endgroup$ – NoThangButtaChknWang Apr 21 at 5:02

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