Figure 3 shows the corresponding plots for ψ$_{a}$ ( x ) and − ψ$_{b}$ ( x ). As one ought expect for a ground state wave function, the upper component ψ$_{a}$ ( x ) has no nodes and the p -wave lower component ψ$_{b}$ ( x ) has one (at the origin). We have plotted the ψ ’s in Fig. 3 this way to compare with GMSS’s Fig. 2. The ψ ’s here are for fitting the non-strange q ¯ q mesons and extend out further than those of GMSS. The reason for that is that GMSS calculated the u and d quark wave functions to fit the non-strange baryon spectrum, which is why they used a value of r 0 = 0 . 57. Physically, the effective origin of the confining potential for mesons is not as strongly localized as in the baryon case, where one more quark damps fluctuations additionally. The procedure outlined in the previous sub-section can be applied to calculate the energy eigenvalues and wave functions for excited states. One expects that the first excited state is the 2 s 1 2 state. This state also has l = 0, l ′ = 1 and k = − 1, so the BCs at x = ϵ are the same as for the 1 s case. The upper component wave function g ( x ) should now have a new node, i.e., cross the x -axis somewhere between the origin and infinity. Thus, if it is desirable to have g ( x ) start off from the origin going positive, one should choose the asymptotic normalization parameter a 1 to be negative. In view of the asymptotic behavior here being similar to that of a simple harmonic oscillator, we might expect that the energy eigenvalue of this state is roughly twice that of the ground state. Choosing the parameters needed for the initial integrations to be the iterative loop again converges in four iterations. The final parameters are ˜ E = 1 . 91897 (i.e., 0.809 GeV) and a 0 = 0 . 378981. Plots of ψ$_{a}$ ( x ) and − ψ$_{b}$ ( x ) are displayed in Fig. 4. For the 2 s 1 / 2 state, ψ$_{a}$ ( x ) has one node and ψ$_{b}$ ( x ) has two. Why are we counting nodes, anyway? Because a state with more nodes has more energy. Qualitatively, more nodes means more curvature, and that means a bigger contribution from ∇ $^{2}$, which in turn means a bigger kinetic energy. Besides the 2 s 1 2 state, there are also two nearby p -wave excited states. The 2 p 3 2 state also has j = l + 1 $_{2}$, but now with l = 1, l ′ = 2, and thus k = − 2. The BCs near the origin 12 ˜ E = 2 . 1 , a 0 = 0 . 3 , a 1 = − 4000 . 0 , (26) F. Some Excited States