We assume that each valence quark in a nucleon is in a phenomenological
modified harmonic oscillator potential of the form: ( l+yo) (ar +br+cr +dr ), where
a, b, c and d are constants and ? is one of the Dirac matrices. Then by making use of
a suitable ansatz, the Dirac equation has a very simple solution which is exact. We
then have calculated the static properties of the nucleon in the ground state with and
without center of mass correction. The results are encouraging. PACS index 12.35
kW and 13.40 fn