  Let $\pi\colon (M,\omega)\to B$ be a non-singular Lagrangian torus fibration
on a complete base $B$ with prequantum line bundle $\bigl(L,\nabla^L\bigr)\to
(M,\omega)$. Compactness on $M$ is not assumed. For a positive integer $N$ and
a compatible almost complex structure $J$ on $(M,\omega)$ invariant along the
fiber of $\pi$, let $D$ be the associated Spin${}^c$ Dirac operator with
coefficients in $L^{\otimes N}$. First, in the case where $J$ is integrable,
under certain technical condition on $J$, we give a complete orthogonal system
$\{ \vartheta_b\}_{b\in B_{\rm BS}}$ of the space of holomorphic $L^2$-sections
of $L^{\otimes N}$ indexed by the Bohr-Sommerfeld points $B_{\rm BS}$ such that
each $\vartheta_b$ converges to a delta-function section supported on the
corresponding Bohr-Sommerfeld fiber $\pi^{-1}(b)$ by the adiabatic(-type)
limit. We also explain the relation of $\vartheta_b$ with Jacobi's theta
functions when $(M,\omega)$ is $T^{2n}$. Second, in the case where $J$ is not
integrable, we give an orthogonal family $\big\{ {\tilde
\vartheta}_b\big\}_{b\in B_{\rm BS}}$ of $L^2$-sections of $L^{\otimes N}$
indexed by $B_{\rm BS}$ which has the same property as above, and show that
each $D{\tilde \vartheta}_b$ converges to $0$ by the adiabatic(-type) limit
with respect to the $L^2$-norm.
