The two-body potential predicted by Lattice QCD is known to be a linear combination of a Coulomb- and a linear potentials. This so called Cornell potential has been of frequent use not only in charmonium spectroscopy but also in the spectroscopy of baryons when considered as quark-di-quark systems. We first make the point that the Cornell potential allows for an extension toward an exactly solvable trigonometric potential of O(4) symmetry. Next we apply the new potential in the calculation of the respective spectra of nucleon and the Delta, considered as quark-diquark systems. We observe that both spectra are reproduced pretty well and that none of the non-strange resonances observed so far drops out of the systematic provided by the trigonometric potential (modulo the hybrid Delta (1600)). Moreover, the number of the missing resonances is significantly reduced. We calculate the proton electric form-factor in terms of a closed expression and find that it follows data with amazing accuracy. We conclude that the complicated quark-gluon dynamics results in a simple exactly solvable trigonometric two-body potential which represents a promising point of departure for more sophisticated studies of baryon properties.
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