  We construct a relativistic potential quark model of $D$, $D_s$, $B$, and
$B_s$ mesons in which the light quark motion is described by the Dirac equation
with a scalar-vector interaction and the heavy quark is considered a local
source of the gluon field. The effective interquark interaction is described by
a combination of the perturbative one-gluon exchange potential
$V_{\mathrm{Coul}}(r)=-\xi/r$ and the long-range Lorentz-scalar and
Lorentz-vector linear potentials $S_{\mathrm{l.r.}}(r)=(1-\lambda)(\sigma
r+V_0)$ and $V_{\mathrm{l.r.}}(r)=\lambda(\sigma r+V_0)$, where
$0\leqslant\lambda<1/2$. Within the quasiclassical approximation, we obtain
simple asymptotic formulas for the energy and mass spectra and for the mean
radii of $D$, $D_s$, $B$, and $B_s$ mesons, which ensure a high accuracy of
calculations even for states with the radial quantum number $n_r\sim 1$. We
show that the fine structure of P-wave states in heavy-light mesons is
primarily sensitive to the choice of two parameters: the strong-coupling
constant $\alpha_s$ and the coefficient $\lambda$ of mixing of the long-range
scalar and vector potentials $S_{\mathrm{l.r.}}(r)$ and $V_{\mathrm{l.r.}}(r)$.
The quasiclassical formulas for asymptotic coefficients of wave function at
zero and infinity are obtained.
