  We use the Dirac equation with a ``(asymptotically free) Coulomb + (Lorentz
scalar) linear '' potential to estimate the light quark wavefunction for $
q\bar Q$ mesons in the limit $m_Q\to \infty$. We use these wavefunctions to
calculate the Isgur-Wise function $\xi (v.v^\prime )$ for orbital and radial
ground states in the phenomenologically interesting range $1\leq v.v^ \prime
\leq 4$. We find a simple expression for the zero-recoil slope, $\xi^ \prime
(1) =-1/2- \epsilon^2 <{r_q}^2>/3$, where $\epsilon$ is the energy eigenvalue
of the light quark, which can be identified with the $\bar\Lambda $ parameter
of the Heavy Quark Effective Theory. This result implies an upper bound of
$-1/2$ for the slope $\xi^\prime (1)$. Also, because for a very light quark $q
(q=u, d)$ the size $\sqrt {<{r_q}^2>}$ of the meson is determined mainly by the
``confining'' term in the potential $(\gamma_\circ \sigma r)$, the shape of
$\xi_{u,d}(v.v^\prime )$ is seen to be mostly sensitive to the dimensionless
ratio $\bar \Lambda_{u,d}^2/\sigma$. We present results for the ranges of
parameters $150 MeV <\bar \Lambda_{u,d} <600 MeV$ $(\bar\Lambda_s \approx
\bar\Lambda_{u,d}+100 MeV)$, $0.14 {GeV}^2 \leq \sigma \leq 0.25 {GeV}^2$ and
light quark masses $m_u, m_d \approx 0, m_s=175 MeV$ and compare to existing
experimental data and other theoretical estimates. Fits to the data give:
${\bar\Lambda_{u,d}}^2/\sigma =4.8\pm 1.7 $, $-\xi^\prime_{u,d}(1)=2.4\pm 0.7$
and $\vert V_{cb} \vert \sqrt {\frac {\tau_B}{1.48 ps}}=0.050\pm 0.008$ [ARGUS
'93]; ${\bar\Lambda_{u,d}}^2/\sigma = 3.4\pm 1.8$, $-\xi^\prime_{u,d}(1)=1.8\pm
0.7$ and $\vert V_{cb} \vert \sqrt { \frac {\tau_B}{1.48 ps}}=0.043\pm 0.008$
[CLEO '93]; ${\bar\Lambda_{u,d}}^2/
