  In this work the $B\bar{B}^*/D\bar{D}^*$ system is studied in the
Bethe-Salpeter approach with quasipotential approximation. In our calculation
both direct and cross diagrams are included in the one-boson-exchange
potential. The numerical results indicate the existence of a isoscalar bound
state $D\bar{D}^*$ with $J^{PC}=1^{++}$, which may be related to the $X(3872)$.
In the isovector sector, no bound state is produced from the interactions of
$D\bar{D}^*$ and $B\bar{B}^*$, which suggests the molecular state explanations
for $Z_b(10610)$ and $Z_c(3900)$ are excluded.
