# Spherical tensor [closed]

These equations are out of Sakurai and Napolitano Modern Quantum Mechanics.

I'm trying to show that $T_q^{(2)}$--which is defined as the bilinear of two vector operators $V_i$ and $W_j$--transforms as a second-rank spherical tensor.

$$T_{\pm2}^{(2)}=U_{\pm1}V_{\pm1}$$

$$T_{\pm1}^{(2)}=\frac{U_{\pm1}V_0+U_0V_{\pm1}}{\sqrt2}$$

$$T_{0}^{(2)}=\frac{U_{+1}V_{-1}+2 \, U_{0}V_{0}+U_{-1}V_{+1}}{\sqrt6}$$

I think I need to show that these vectors transform properly under rotations, but I'm not exactly sure. Any help would be appreciated.

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 Hi Alex - this is a site for conceptual questions about physics, not general homework help. If you can edit your question to ask about the specific physics concept that is giving you trouble, I'll be happy to reopen it. See our FAQ and homework policy for more information. (Alternatively, perhaps this could be migrated to Mathematics) – David Zaslavsky♦ Dec 9 '12 at 22:38

## closed as too localized by David Zaslavsky♦Dec 9 '12 at 22:38

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