where l ′ = 2 j − l and the Y l jm are the spin-orbital angular momentum wave functions, where < jm | l 1 $_{2}$, m − m$_{s}$ m$_{s}$ > is a Clebsch-Gordan coefficient and χ is a Pauli spinor. We consider here the case of bound-state wave functions for a central potential with energy eigenvalue E . For example, for hydrogen-like atoms the potential is V$_{v}$ ( r ) = − Zα/r . With appropriate boundary conditions, the radial wave functions g ( r ) and f ( r ), which can be taken as real functions, are solutions of the following coupled first-order ordinary differential equations (ODEs), [9, 12] Here the integer k is determined by the angular momentum quantum numbers according to The reason for the subscript on the potential V$_{v}$ in those equations is to indicate that it is the fourth component of a Lorentz four-vector, such as the Coulomb potential. However, our motivation is not so much in atomic physics applications as it is for treating mesons as q ¯ q states in a relativistic quark model. The non -relativistic quark model often assumes the confining potential for quarks to be the so-called “Cornell potential,” [6] where α$_{s}$ = g 2 s / 4 π , with g$_{s}$ being the (running) quark-gluon coupling constant, and κ 2 (or σ ) is the string tension. It is the linear term in V ( r ) that confines the quarks, corresponding to the effective potential in the relativistic Bag Model.[2] For a relativistic quark model, the two pieces of that non-relativistic potential have dif- ferent Lorentz transformation properties. The color Coulomb potential, α$_{s}$/r , is the fourth component of a Lorentz vector, while the confining linear potential transforms as a Lorentz scalar, which we will write as V$_{s}$ ( r ). Thus, in solving the relativistic radial Dirac equations, 3 V ( r ) = − α$_{s}$ r + κ $^{2}$r , (6) g $^{′}$( r ) + k r g ( r ) − ( E − V$_{v}$ ( r ) + m ) f ( r ) = 0 , (3) f $^{′}$( r ) − k r g ( r ) + ( E − V$_{v}$ ( r ) − m ) g ( r ) = 0 . (4) Y l ′ $_{jm}$( θ, φ ) = ∑ m s < jm | l 1 $_{2}$, m − m$_{s}$ m$_{s}$ > Y l $_{m}$( θ, φ ) χ$_{m}$ s , (2) k = − ( l + 1) if j = l + 1 2 , k = l if j = l − 1 2 . (5)