# How to understand notation in “Introduction to Quantum Mechanics (3rd Edition)” by David Griffiths, Chapter 3.6.2?

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:

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

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