Steve Zelditch

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Eigenfunctions of the Schrodinger operator (or a Laplacian on a domain or manifold)
represent modes of vibrations of drums and membranes. In quantum mechanics
they represent stationary states of atoms. Understanding shapes and sizes of
eigenfunctions allows one to visualize these objects. An intriguing problem
is to relate the shapes and sizes of eigenfunctions to the underlying classical mechanics,
such as the geodesic flow of (M, g) or the dynamics of billiard trajectories
on a billiard table.

In this talk we will explain the role of eigenfunctions in quantum mechanics
and discuss both classic and new results describing nodal (zero) sets
of eigenfunctions. The new results relate nodal sets to classical dynamics.
No prior knowledge of quantum mechanics is assumed.

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Northwestern University
Seminar Room of the Institute of Physics II (R201)
Contact: George Marinescu