  By making use of an ${\it ansatz}$ for the eigenfunction, we obtain the exact
solutions to the Schr\"{o}dinger equation with the anharmonic potential,
$V(r)=a r^2+b r^{-4}+c r^{-6}$, both in three dimensions and in two dimensions,
where the parameters $a$, $b$, and $c$ in the potential satisfy some
constraints.
