Scattering at threshold in massive wave propagation and ionization
Name
sussman-ethanws-phd-math-2023-thesis-pdf.pdf
Description
Thesis PDF
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3.73 MB
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Adobe PDF
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ea0607483e9201ba6a4059542c160c79
Author(s)
Sussman, Ethan W.
Advisor(s)
Hintz, Peter
Date Issued
June 2023
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, we examine the transition between Legendrian regularity and ellipticity at infinity for two PDEs, the Schrödinger–Helmholtz equation with an attractive long range potential and the Klein–Gordon equation. In the former case, the transition occurs as the spectral parameter 𝐸 → 0⁺, and thus describes the ionization of Hydrogenic atoms, and in the latter case the transition occurs at null infinity, where the phase in the asymptotic tails becomes singular. Using novel microlocal tools, we work in the variable coefficient setting throughout.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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