A physical example approximating the idealized situation

[ENDLESSYOU]

From Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, Eisberg-Resnick:
"A physical example approximating the idealized situation represented by these
wave functions would be a proton moving in a highly monoenergetic beam emerging
from a cyclotron. Such beams are used to study the scattering of protons by targets
of nuclei inserted in the beam. From the point of view of the target nucleus, and in
terms of distances of the order of its nuclear radius r', the x position of a proton in
the beam may be for all practical purposes completely unknown. That is Δx » r'.
...In other words, near a nucleus the wave function of (6-9)
$ψ = Ae^{i(kx - wt)}$
can be used to describe a proton in a cyclotron beam directed towards increasing x,
providing the beam is extremely long compared to the dimensions of the nucleus—a
condition which is always satisfied in practice since nuclei are extremely small."
I don't understand why "the x position of a proton in the beam may be for all practical purposes completely unknown".
Thanks!

 

[mfb]

Typical beams have a width of micrometers to millimeters, while the target nucleus has a size of femtometers. Even if you look at a single proton in the beam, its wavefunction will be spread out extremely wide compared to the size of a nucleus.