V. SUMMARY In this paper we have discussed, pedagogically, three increasingly more sensitive cases for solving the radial Dirac equations numerically: 1. A Lorentz scalar potential, V$_{s}$ , which is linearly confining for quarks. The case of massless quarks is necessarily relativistic. As the mass of the quark increases, the wave function solutions become more and more n0n-relativistic. 2. A Lorentz vector potential, V$_{v}$ , whose time-like component is a Coulomb potential. We first treated, numerically, the hydrogen atom, which is basically non-relativistic problem. We do, however, obtain the relativistic spin-orbit splitting between the 2 p 1 2 and 2 p 3 2 states (at the edge of our machine precision). 3. The combination of scalar and vector potentials, aiming at a relativistic quark model of mesons. Of particular interest is when we do (and do not) get a relativistic spin-orbit splitting. [1] P. A. M. Dirac, Proc. Roy. Soc. (London), A117 , 610 (1928) and A118 , 351 (1928). [2] C. E. DeTar, J. F. Donoghue, Bag Models Of Hadrons , Ann. Rev. Nucl. Part. Sci., 235-264 (1983). [3] A. W. Thomas, S. Teberge, and G. A. Miller, Phys. Rev. D 24 , 216 (1981); D. B. Leinweber, A. W. Thomas, and R. D. Young, Phys. Rev. Lett. 86 , 5011 (2001). [4] T. Goldman, K. R. Maltman, G. J. Stephenson, Jr., and K. E. Schmidt, Nucl. Phys. A481 , 621 (1988). This reference is henceforth abbreviated as GMSS. [5] K. Saito and A. W. Thomas, Phys. Lett. B 327 , 9 (1994); P. A. M. Guichon, K. Saito, E. N. Rodionov, and A. W. Thomas, Nucl. Phys. A ¯ 601, 349 (1996). [6] E. E. Eichten et al., Phys. Rev. Lett. 34 , 369 (1975); Phys. Rev. D 17 , 3090 (1978); Phys. Rev. D 21 , 203 (1980). [7] L. L. Foldy and S. A. Wouthuysen, Phys. Rev. 78 , 29 (1950). 25 We thank L. J. Curtis, J. L. Friar, C. J. Fontes, M. D. Scadron, and R. Sharma for discussions and comments on this work.