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Since effective potentials derived from Feynman diagrams are naturally givenin momentum space, we formulate the non-relativistic Coulomb problem entirelyin momentum representation. We give momentum wave functions for all quantumnumbers in one-dimensional integrals, even though they can be evaluated.Angular momentum decomposed Green's functions are then compactly represented.We apply this formalism to investigate the next to next leading order charmeffects on 1S bottomonium level shift. Our one insertion results are givencompletely in analytic form and numerically agree with previous results. Ourtwo insertion results are also in agreement. The net effect of finite charmmass is to decrease the bottom mass by 33 MeV, as determined through themeasured 1S energy.Comment: We oversight a term in eq.(106). After adding this term, our result  agree with that in ref.[6

Momentum representation of Coulomb wave functions and level shifts in bottomonium due to charm effects