I Is this PDF file the correct derivation?

[oliverkahn]

TL;DR Summary

Given: Potential $\psi(r)=constant$
To prove: $u(r)=k_1+\dfrac{k_2}{r}$

My work is in the following pdf file:

 

[mfb]

There is a lot of context missing.

 

[oliverkahn]

Oh! I see. I was too hasty...Let me add some extra material in the beginning.