Imagine preparing a particle in a "position eigenstate" $|x_0\rangle$. Its momentum-space wave function would be $\phi(p) = \langle p|x_0\rangle = \frac{1}{\sqrt{2\pi\hbar}}e^{-ipx_0/\hbar}$, a plane wave of constant amplitude. The probability density $|\phi(p)|^2 = 1/(2\pi\hbar)$ is uniform — every