Two relativistic quark models wth a harmonic oscillator potential

Two relativistic quark models are presented, one based on the Klein-Gordon equation, and the other, on the Dirac equation. In the first model the quark-antiquark interaction is taken to be a harmonic oscillator potential that behaves as the fourth component of a four-vector. The bound-state meson mass spectra are calculated using the WKB approximation method. The resulting mass spectra are not significantly different from those obtained by Kang and Schnitzer using a linear potential. In the second model, the harmonic oscillator potential is used as a scalar. This approach is equivalent to generalizing the mass as m(r) = μ + a3r2. The energy values turn out to be complex, and become almost real for values of μ/a greater than or equal to about 2