Angular momentum in bracket notation

[Alexis21]

Hello,

why is

$<j' m' | j m>=0$

if

$j \not= j' \; \text{or} \; m \not= m'$

j and m are describing states. I don't understand why an 'empty bracket' behaves like that.

 

[phyzguy]

This just says that the angular momentum eigenstates form an orthogonal set, so the inner product of any two is zero unless they are the same. You might read this:

http://en.wikipedia.org/wiki/Spherical_harmonics#Orbital_angular_momentum