Mathematical counterpart of the heisenberg uncertainty principle

In this paper we provide an exposition on integrability theorem and relation between D-modules and symplectic geometry. We prove that the characteristic ideal of a module over the Weyl algebra with Bernstein and order filtrations is closed under the Poisson bracket. This result can be viewed as a mathematical counterpart of the heisenberg uncertainty principle. Several examples have been explained in detail to understand this important deep result and related concepts.