The momentum operator for one spatial dimension is $-i \hbar\frac{\mathrm d}{\mathrm dx}$ (which isn't a vector operator) but for 3 spatial dimensions is $-i\hbar\nabla$ which is a vector operator. So is it a vector or a scalar operator?
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Momentum is a vector operator. Period.
When restricted to one-dimensional problems, momentum becomes a one-dimensional vector, which coincides with scalars in that space.
Emilio Pisanty
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$-i\hbar \frac{d}{dx}$, a scalar, is the position space representation of $\hat{p}_x$, the $x$ component of the momentum operator, a scalar. The momentum operator itself, $\hat{\textbf{p}}$, is a vector operator. The position space representation of $\hat{\textbf{p}}$ would be $-i\hbar \nabla$, a vector.
Again, the momentum operator is a vector operator. The components of the momentum operator are scalars operators.
Jagerber48
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