A quadratic potential in a light cone QCD inspired model

Abstract

The general equation from previous work is specialized to a quadratic potential $V(r)=-a+\frac{1}{2}f{r}^2$ acting in the space of spherically symmetric S wave functions. The fine and hyperfine interaction creates then a position dependent mass $\tilde{m}(r)$ in the effective kinetic energy of the associated Schrödinger equation. The results are compared with the available experimental and theoretical spectral data on the $\pi$ and $\rho$. Solving the eigenvalue problem within the usual oscillator approach induces a certain amount of arbitrariness. Despite of this, the agreement with experimental data is within the experimental error and better than other calculations, including Godfrey and Isgur \cite{GodIsg85} and Baldicchi and Prosperi \cite{BalPro02}. The short coming can be removed easily in more elaborate work.

Comments: LaTeX2e, 4 pages, 11 references. Paper 5 of 5