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

I have read the follow bock

http://books.google.cl/books?id=BPCFI4yFMbcC&pg=PA8&lpg=PA8&dq=Jz+2+matrix+"cartesian+basis"&source=bl&ots=-h9EHPssXf&sig=Mk97jJ55GctKfPAkViMNT7N7erE&hl=es-419&sa=X&ei=nK9BU6jXAdDnsASetYKAAg&ved=0CGYQ6AEwBw#v=onepage&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

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

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