Scattering at threshold in massive wave propagation and ionization

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.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2023

Author dc:creator

• Sussman, Ethan W.

Advisor dc:contributor.advisor

• Hintz, Peter

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright retained by author(s)

Licence dc:rights.uri

• https://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/151508

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/151508