How does one calculate an explicit form for the irreducible tensor operators in a given basis? In my particular case, I'm looking at expanding a 3X3 density matrix in the angular momentum basis. T_1n (n = -1, 0, 1) are simple enough : J+, J_z, J-. But what about T_2n (n = -2 ... 2)? I know the answer, but don't know how it was arrived at...

Clues?

(Note : '_', as usual, indicates that what follows is a subscript)

Oh - and if you can help out with a physical significance for the T_2n I would appreciate it. Again - T_1n are angular momenta, but T_2n???