Mathematics Colloquium 09-27-01
Mathematics Colloquium
Thursday, September 27 at 4pm in 317 Kerchof Hall
Steve Zelditch
(Johns Hopkins University)
"Highly excited quantum states"
Abstract:
This talk is about excited states of quantum systems, i.e.
eigenfunctions of Laplacians
or Schrodinger operators on Riemannian manifolds
in the `high energy' limit as the eigenvalue tends
to infinity. We are especially concerned with the size of the
eigenfunctions (as measured
in L^p), and the distribution of their zeros (nodal sets) and critical
points. The
main theme is how the global geometry of a Riemannian manifold influences
the morphology of its eigenfunctions.
I will present several new results illustrating the influence
(obtained in collaboration with B. Shiffman, C. Sogge
and J. Toth.) I will also present slides illustrating the excited states
in a number of settings of mathematical and physical interest.
Refreshments at 3:30 in 314 Kerchof Hall