Regarding an approximation of p as 1 over r

[14lawrenze]

Homework Statement

estimate the ground energy of a bound qqbar system , the total hamiltonian can be written as ,
H(r)=2m-a/r+br+p^2/m,where a=0.5, b=0.18Gev^2, m being the mass of quark or antiquark the book kinds of gives Hint " p may be approximated as 1 over r" ,natural unit is assumed ,(c=hbar=1)

Homework Equations

In particular , my question ," why we could always argue that p may be approximated as 1 over r" the uncertainty principle can be essentially delivered by an inequalitiy deltax*deltap>=1/2, where deltax is understood as x-<x>, it imposes , according to the widely accepted understanding of quantum physics, an upper limit to the degree of precision we may
reach in measurement . nevertheless , in "this "homework " , why we'd just approximate p as 1 over r , as we do all the time , like we argue that an electron may never fall into nucleus.
we seem to always approximate momentum as inverse r , and that is why?
sorry for the sloppy language ,and it's technically a homework problem , I wanted to post it in other sections ,though.

The Attempt at a Solution

 

[Nate810]

I am trying to solve this problem , but I just find it odd that we can always approximate the momentum as inverse r