The boundary conditions (BC’s) at the origin for this smeared Coulomb potential (for angular momentum j = l + 1 $_{2}$) now become Running the program with α$_{s}$ = 0 . 4 and the above R gives curves for ψ$_{a}$ ( x ) and − ψ$_{b}$ ( x ) with similar upturns and falloffs near the origin as in Fig. 18, but less sharply so. One should be aware that, while interesting, these differences in the ψ$_{a,b}$ ( x ) near the origin make only minor differences in expectation values of operators because of the factor of x 2 in the integration over d $^{3}$x ; see, e.g., the normalization condition, Eq. (12). For this smeared potential, the eigenenergies and final a 0 parameters for various values of α$_{s}$ are also tabulated in Table II. As expected from the above remark, the energy expectation value is basically unchanged from the point Coulomb value until one reaches the point where the quark condensate takes over. However, the initial slope parameters a 0 do differ from those of the point Coulomb case, being less pathological as E goes through zero. In this subsection we will assume both potentials V$_{s}$ ( x ) and V$_{v}$ ( x ) are linearly confining and have the same slopes (i.e., have the same string tension κ $^{2}$). We assume the two potentials are displaced from each other with V$_{s}$ ( x ) lying above V$_{v}$ ( x ), as in Fig. 19. That is, we assume or, more appropriately, the smeared version of V$_{v}$ ( x ) as described above in Sec. IV A. Here x$_{s}$ and x$_{v}$ are parameters to be adjusted to get some desired eigenenergy. They give rise to a separation between the two asymptotic potentials of x$_{d}$ = x$_{s}$ + x$_{v}$ . The reason for giving the potentials the same asymptotic slopes is to check that the spin-orbit interaction disappears as claimed in Ref. [25]. In doing so, we have changed the earlier offset of − x 0 in V$_{s}$ to + x$_{s}$ since, in GMSS (where only a Lorentz scalar potential was used), the negative offset − x 0 represented a reasonable approximation the one-gluon- exchange attraction, roughly an average of the two potentials as shown in the figure. Now, however, the BC’s at large distances are changed from those in Eq. (16), since, in the equation for g ( x ), Eq. (7), the difference of the dimensionless V$_{s}$ ( x ) and V$_{v}$ ( x ) → x has 22 V$_{s}$ ( x ) = x + x$_{s}$, V$_{v}$ ( x ) = − α$_{s}$/x + x − x$_{v}$ , (51) g ( ϵ ) = a 0 ϵ l $^{+1}$, f ( ϵ ) = − a 0 ( ˜ E − V$_{v}$ ( ϵ ) − V$_{s}$ ( ϵ ) − ˜ m ) ϵ l $^{+2}$/ (2 l + 3) . (50) B. V$_{v}$ as the Cornell Potential and the Spin-orbit Force.