# Another physical question

Hi, I am wondering what justifies the substitution p_x -> (h/i)d/dx ? I know it is very common but I have not seen a reason for it anywhere. Why does it make physical sense?

For a plane wave, that is $\psi(x) = e^{i k x}$, $\frac{1}{i} d/dx$ extracts the wave vector or wavenumber $k$of the wave. From there we use de Broglie's relation to get the $$\hbar$$.