A linear potential in a light cone QCD inspired model

Abstract

The general equation from previous work is specialized to a linear potential $V(r)=-a+F r$ acting in the space of spherically symmetric S wave functions. The fine and hyperfine interaction creates then a $\frac1r$-dependence in the effective potential energy equation and a position dependent mass $\widetilde m(r)$ in the effective kinetic energy of the associated Schr\"odinger equation. The results are compared with the available experimental and theoretical spectral data on the $\pi$ and $\rho$. Solving the eigenvalue problem within the analytically tractable Airy-function approach induces a certain amount of arbitrariness (fudge factors). Despite of this, the agreement with experimental data is good and partially better than other calculations, including Godfrey and Isgur \cite{GodIsg85} and Baldicchi and Prosperi \cite{BalPro02}. The short comings of the present model can be removed easily in more elaborate work.