  We study rational Lagrangian immersions in a cotangent bundle, based on the
microlocal theory of sheaves. We construct a sheaf quantization of a rational
Lagrangian immersion and investigate its properties in Tamarkin category. Using
the sheaf quantization, we give an explicit bound for the displacement energy
and a Betti/cup-length estimate for the number of the intersection points of
the immersion and its Hamiltonian image by a purely sheaf-theoretic method.

Symplectic Geometry