Prove that the operator \(a_{j m}^{\dagger}\) that acts on the vacuum as \(a_{j m}^{\dagger}|0angle=|j mangle\) to create a fermion with angular momentum \(j\) and magnetic quantum number \(m\) transforms as a spherical tensor of rank \(j\). The second-quantized form of the angular momentum operator is

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Ja = (a Ja) aa a where a and label single-particle states, and fermion operators obey {a,, a}} = 8, and {a, a} = {a,,a; } = 0.