The University of Arizona
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On a discretization of the Schrödinger equation

Mathematical Physics and Probability Seminar

On a discretization of the Schrödinger equation
Series: Mathematical Physics and Probability Seminar
Location: MATH 402
Presenter: Alex Loomis, University of Arizona

We consider the Many Interacting Worlds (Hall, Deckert, Wiseman 2014) discretization of Schrodinger's equation on R, leading to a N particle Hamiltonian system. It is known that the empirical measure of the ground state of the discrete system converges to a Normal distribution, the ground state of the continuum system (McKeague, Levin 2016). In this talk, we consider N particle states, naturally given, which approximate the higher order energies in the discrete system, and whose empirical measures converge to the higher order energy states of the continuum system, such as the Maxwellian etc. The method is by Stein's method, which shows convergence of the empirical measures in Wasserstein distance.

(zoom link: https://arizona.zoom.us/j/81196695512)