Question: Prove that the 3D harmonic oscillator orbital angular momentum operators are given by (boldsymbol{L}=i boldsymbol{a} times boldsymbol{a}^{dagger}). Show that the components (L_{k}) obey the commutator

Prove that the 3D harmonic oscillator orbital angular momentum operators are given by $\boldsymbol{L}=i \boldsymbol{a} \times \boldsymbol{a}^{\dagger}$. Show that the components $L_{k}$ obey the commutator (10.13).

Data from Eq. 10.13

[L, a]] = iejka,

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