  We make the case that the Coulomb- plus linear quark confinement potential
predicted by lattice QCD is an approximation to the exactly solvable
trigonometric Rosen-Morse potential that has the property to interpolate
between the Coulomb- and the infinite wells. We test the predictive power of
this potential in the description of the nucleon (considered as a quark-diquark
system) and provide analytic expressions for its mass spectrum and the proton
electric form factor. We compare the results obtained in this fashion to data
and find quite good agreement. We obtain an effective gluon propagator in
closed form as the Fourier transform of the potential under investigation.
