It is considered that the effective interaction between any two quarks of a baryon can be approximately described by a simple harmonic potential. The problem is firstly solved in Cartesian coordinates in order to find the energy levels irrespective of their angular mo- menta. Then, the problem is also solved in polar cylindrical coordinates in order to take into account the angular momenta of the levels. Comparing the two solutions, a correspon- dence is made between the angular momenta and parities for almost all experimentally determined levels.

The agreement with the experimental data is quite impressive and, in general, the discrepancy between calculated and experimental values is below 5%. A cou- ple of levels of ∆, N, Σ±, and Ω present discrepacies between 6.7% and 12.5% [N(1655), N(1440), N(1675), N(1685), N(1700), N(1710), N(1720), N(1990), N(2600), ∆(1700), ∆(2000), ∆(2300), Σ±(1189), Λ(1520), Ω(1672) and Ω(2250)].

* [Article published in January, 2016]*