  We investigate the $B$ and $D$ mesons in the relativistic quark model by
applying the variational method with the Gaussian wave function. We calculate
the Fermi momentum parameter $p_{_F}$, and obtain $p_{_F} = 0.50 \sim 0.54$
GeV, which is almost independent of the input parameters, $\alpha_s$, $m_b$,
$m_c$ and $m_{sp}$. We then calculate the ratio $f_B$/$f_D$, and obtain the
result which is larger, by the factor of about 1.3, than $\sqrt{M_D / M_B}$
given by the naive nonrelativistic analogy. This result is in a good agreement
with the recent Lattice calculations. We also calculate the ratio
$(M_{B^*}-M_{B})$/$(M_{D^*}-M_{D})$. In these calculations the wave function at
origin $\psi (0)$ is essential. We also determine $p_{_F}$ by comparing the
theoretical prediction of the ACCMM model with the lepton energy spectrum of $B
\rightarrow e \nu X$ from the recent ARGUS analysis, and find that
$p_{_F}=0.27~\pm~^{0.22}_{0.27}$ GeV, when we use $m_c=1.5$ GeV. However, this
experimentally determined value of $p_{_F}$ is strongly dependent on the value
of input parameter $m_c$.
