= Spherical tensor operator
{title2=$T_q^{(k)}$}
A rank-$k$ <spherical tensor operator> has components $T_q^{(k)}$, $-k\leq q\leq k$, that transform under <rotation> like an <angular momentum> $k$. Equivalently, their <commutators> with the <angular momentum operator> satisfy
$$
[J_z,T_q^{(k)}]=\hbar qT_q^{(k)},\qquad
[J_\pm,T_q^{(k)}]=\hbar\sqrt{k(k+1)-q(q\pm1)}\,T_{q\pm1}^{(k)}.
$$
For a vector operator, the rank is one and a conventional choice is $T_0=V_z$, $T_{\pm1}=\mp(V_x\pm iV_y)/\sqrt2$. The <Wigner-Eckart theorem> separates the <matrix elements> of a <spherical tensor operator> into <Clebsch-Gordan coefficients> and a <reduced matrix element>.
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