{wiki}

One dimension in <position representation>:
$$
\hat{p} = - i \hbar \pdv{}{x}
$$

In three dimensions In position representation, we define it by using the <gradient>, and so we see that 
$$
\hat{p} = - i \hbar \pdv{}{x}
$$

\Video[https://www.youtube.com/watch?v=Egu4i8umpoM]
{title=Position and Momentum from Wavefunctions by <Faculty of Khan> (2018)}
{description=Proves in detail why the <momentum operator> is $\pdv{}{x}$. The starting point is determining the time <derivative> of the <expectation value> of the <position operator>.}


 Momentum operator