of finite-range bound states in the context of this model of confinement. The numerical evaluation of the QPV for both the time-like and space-like regions of the photon momentum squared is given in Sec.4. Finally, a summary is presented in Sec.5.

General features
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The inhomogeneous Bethe-Salpeter equation
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In this section, the steps required to reduce the inhomogeneous Bethe-Salpeter equation (\[IBS\]) to a form suitable for computer applications are outlined. The approach is straightforward and is based on the general features of the QPV as described by (\[IBS\]). Where possible, lengthy algebraic manipulations are omitted. To begin, it is useful to write the self energy, $\Sigma $ from (\[SDE\]), in the form $$\Sigma (P)=i\! \not \! P\left[ A(P^2)-1\right] +B(P^2)\label{2.1}$$ where $$\left[ A(P^2)-1\right] P^2= g^2\frac{8}{3}\int \frac{d^4K}{(2\pi
)^4}D(P-K)\frac{A(K^2)P\cdot K}{K^2A^2(K^2)+B^2(K^2)},\label{2.2}$$ and $$B(P^2)=g^2\frac{16}{3}\int \frac{d^4K}{(2\pi
)^4}D(P-K)\frac{B(K^2)}{K^2A^2(K^2)+B^2(K^2)}.\label{2.3}$$ The quark Green’s function, $G$, and its inverse, $G^{-1}$, can then be written as $$G(P)=-i\! \not \! P \alpha (P^2)+\beta (P^2)\; \; \; \; \; \mbox{and}
\; \; \; \; \;G^{-1}(P)=i\! \not \! PA(P^2)+B(P^2),\label{2.4}$$ where $\alpha $ and $\beta $ are defined in an obvious fashion from $G^{-1}$.

From Eq.(\[IBS\]) it is evident that the QPV, in addition to its Lorentz four-vector structure, is a four-by-four matrix in 