SEMINAR: Honours Seminar

This dissertation presents and expands on a seminal result of A.I. Schnirelman in the theory of quantum ergodicity. The theorem is concerned with the probability densities defined by eigenfunctions of the Laplace-Beltrami operator on a compact Riemannian manifold. An example of semiclassical correspondence, it asserts, for an ergodic geodesic flow, the existence of a sequence of these functions for which the densities are asymptotically uniform in the limit of high eigenvalues. The theories of pseudodifferential operators, distributions, symplectic geometry and ergodic systems are developed in the earlier chapters, as these are relied on heavily in the theorem's proof.