  Let $X$ be a compact Kahler manifold and $L\to X$ a quantizing holomorphic
Hermitian line bundle. To immersed Lagrangian submanifolds $\Lambda$ of $X$
satisfying a Bohr-Sommerfeld condition we associate sequences $\{ |\Lambda,
k\rangle \}_{k=1}^\infty$, where $\forall k$ $|\Lambda, k\rangle$ is a
holomorphic section of $L^{\otimes k}$. The terms in each sequence concentrate
on $\Lambda$, and a sequence itself has a symbol which is a half-form,
$\sigma$, on $\Lambda$. We prove estimates, as $k\to\infty$, of the norm
squares $\langle \Lambda, k|\Lambda, k\rangle$ in terms of $\int_\Lambda
\sigma\overline{\sigma}$. More generally, we show that if $\Lambda_1$ and
$\Lambda_2$ are two Bohr-Sommerfeld Lagrangian submanifolds intersecting
cleanly, the inner products $\langle\Lambda_1, k|\Lambda_2, k\rangle$ have an
asymptotic expansion as $k\to\infty$, the leading coefficient being an integral
over the intersection $\Lambda_1\cap\Lambda_2$. Our construction is a
quantization scheme of Bohr-Sommerfeld Lagrangian submanifolds of $X$. We prove
that the Poincar\'e series on hyperbolic surfaces are a particular case, and
therefore obtain estimates of their norms and inner products.
