  An important problem in geometric quantization is that of quantizing certain
classes of Lagrangian submanifolds, so-called Bohr-Sommerfeld Lagrangian
submanifolds, equipped with a smooth half-density. A procedure for this in the
complex projective setting is, roughly speaking, to apply the Szego kernel of
the quantizing line bundle to a certain induced delta function supported on the
submanifold. If the quantizing line bundle L is replaced by its k-th tensor
power, and k tends to infinity, the resulting quantum states u_k concentrate
asymptotically on the submanifold. This note deals with the scaling asymptotics
of the u_k's along the submanifold; in particular, we point out a natural
factorization in the corresponding asymptotic expansion, and provide some
remainder estimates.
