Matriz Lz, m=2, but in x,y,z basis

[alejandrito29]

I have read the follow bock

http://books.google.cl/books?id=BPC...epage&q=Jz 2 matrix "cartesian basis"&f=false

The matrix $J_z$, J=1, in spherical armonics is diag(1,0,-1) but in the cartesian basis is i h(0,-1,0)(1,0,0),(0,0,0)

The j_z matriz in spherical harmonics basis is diag (2,1,0,-1,-2), ¿hoy is the J_z matrix, j=2, but in cartesian basis?

 

[DrClaude]

I don't see how you can map $J=2$ to three-dimensional cartesian space.