Canonical momentum is defined as:
$${\displaystyle p_{j}={\frac {\partial {\mathcal {L}}}{\partial {\dot {q}}_{j}}}\,}.$$
In quantum mechanics, momentum is a differential operator:
$${\displaystyle {\hat {p}}=-i\hbar {\frac {\partial }{\partial x}}}.$$
Can I somehow obtain the momentum operator from the canonical momentum, via canonical quantization or something similar or do I have to take it as a definition?
