In the lecture, my professor wrote:

With potential $V(x)=-Fx$, where $F$ is a constant, in momentum space the Schrodinger equation takes the form $$ \left[\frac{p^2}{2m}-i\hbar F\frac{d}{dp}\right]\varphi_E(p)=E\varphi_E(p) $$

I know I have to transform the potential using Fourier transform, but I don't get $V(p)=-i\hbar F\frac{d}{dp}$. Can someone explain how he gets $V(p)$?

Thank you very much!


This is a straightforward substitution. In momentum space the position operator is:

$$ \hat{x} = i \hbar \frac{d}{dp} $$

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