Title: The Weber equation as a normal form with applications to top of the barrier scattering
Speaker: Rodica Costin (OSU)
Abstract: We revisit the 1-dimensional Schrodinger equation for energy near the unique maximal value of the potential, a problem already investigated by many authors. We show that the problem is reducible to a Weber normal form by means of the Liouville-Green transform. We show that the diffeomorphism which effects this stretching of the independent variable lies in the same regularity class as the potential (analytic or infinitely differentiable) with respect to both variables, i.e., space and energy. We then apply the Weber normal form to the scattering problem for energies near the potential maximum. In particular we obtain a representation of the scattering matrix which is accurate up to multiplicative factors of the form 1 + o(1). Joint work with Hyejin Park (OSU) and Wilhelm Schlag (University of Chicago).
Seminar URL: https://research.math.osu.edu/aot/