Spherical harmonics and angular momentum operators

[FarticleFysics]

When solving for the spherical harmonic equations of the orbital angular momentum this textbook I'm reading..

Does this mean that there must be a max value of Lz which is denoted by |ll>? Normally the ket would look like |lm>, and since m is maxed at m=l then |ll> is the ket consisting of the eigenvectors for the max values of the orbital angular momentum.

Also how do we know the associated eigenvalues of Lz look like l h_bar?

 

[Simon Bridge]

Does this mean that there must be a max value of Lz which is denoted by |ll>

It doesn;t matter - all they care about is that it is an eigenvector of Lz.

Also how do we know the associated eigenvalues of Lz look like l h_bar?

... because that is always what they look like - should have been covered earlier in the text.

$\renewcommand{\ket}[1]{| #1 \rangle}$
$L_z\ket{l,m}=m\hbar\ket{l,m}$

http://en.wikipedia.org/wiki/Angula...tal_angular_momentum_in_spherical_coordinates

 

[FarticleFysics]

Yes, I did the derivation of the eigenvalues as well. Thanks for your help!

 

[Simon Bridge]

Well done!