  Let V be a symplectic vector space and LG be the Lagrangian Grassmannian
which parametrizes maximal isotropic subspaces in V. We give a presentation for
the (small) quantum cohomology ring QH^*(LG) and show that its multiplicative
structure is determined by the ring of (Q^~)-polynomials. We formulate a
"quantum Schubert calculus" which includes quantum Pieri and Giambelli
formulas, as well as algorithms for computing the structure constants appearing
in the quantum product of Schubert classes.
