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Qmechanic
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QM: How to get the position operator in terms ofthe momentum representation from knowing the momentum operator in the position representation?

I know that

$$\tag{1}\hat{p}~=~-i\hbar \frac{\partial}{\partial x}~.$$

How can I get

$$\tag{2}\hat{x}~=~i\hbar \frac{\partial}{\partial p}~?$$

I think this simple and I'm just over thinking it, but knowing the momentum operator (1), how can I get the position operator (2)? I know $$\hat{p}=-ih \frac{\partial}{\partial x}$$ How can i get $$\hat{x}=ih \frac{\partial}{\partial p}$$

QM: position operator in terms of momentum

I think this simple and I'm just over thinking it, but knowing the momentum operator, how can I get the position operator? I know $$\hat{p}=-ih \frac{\partial}{\partial x}$$ How can i get $$\hat{x}=ih \frac{\partial}{\partial p}$$

How to get the position operator in the momentum representation from knowing the momentum operator in the position representation?

I know that

$$\tag{1}\hat{p}~=~-i\hbar \frac{\partial}{\partial x}~.$$

How can I get

$$\tag{2}\hat{x}~=~i\hbar \frac{\partial}{\partial p}~?$$

I think this simple and I'm just over thinking it, but knowing the momentum operator (1), how can I get the position operator (2)?

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user34032
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QM: position operator in terms of momentum

I think this simple and I'm just over thinking it, but knowing the momentum operator, how can I get the position operator? I know $$\hat{p}=-ih \frac{\partial}{\partial x}$$ How can i get $$\hat{x}=ih \frac{\partial}{\partial p}$$