= Solution
The <orbital angular momentum> <linear operator> is the cross product of the <position operator> and the <momentum operator>:
$$
\boxed{\widehat{\mathbf L}=\widehat{\mathbf r}\times\widehat{\mathbf p},\qquad \widehat L_i=\sum_{j,k}\varepsilon_{ijk}\widehat x_j\widehat p_k.}
$$
In position space, $\widehat{\mathbf p}=-i\hbar\nabla$, so $\widehat{\mathbf L}=-i\hbar\,\mathbf r\times\nabla$. The <Levi-Civita symbol> gives $\widehat L_1=\widehat x_2\widehat p_3-\widehat x_3\widehat p_2$ and its cyclic analogues.
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