Quick Dirac Notation question - (maths)

[square_imp]

Got a question as follows:

<aaa/aab> where the slash is meant to be a straight line down and a is alpha and b is beta. Alpha and Beta are orthogonal.

In this case can you work out the bra-ket by doing each pair, i.e aa = 1, aa = 1, ab = 0 ? Giving an answer of zero? I am not really sure. Alpha and Beta are the two states for nucleon spin.

generally any help is much appreciated.

Square

 

[square_imp]

<aaa|aab> = (<a| x <a| x <a|)(|a> x |a> x |b>) = <a|a><a|a><a|b> = 0.

To make it clearer you could add suffices to the bras and kets (1,2,3 for each particle, then the 1 bras only act on the 1 kets etc.)

However, I'm not entirely sure about this.

that was my main question about whether the above manipulation is valid, then the problem is fine.

thanks for the help.