Sunday, 16 August 2015

quantum mechanics - 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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