2026-09-21T02:58:13Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1515082023-08-01T03:08:13Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Hintz, Peter
Sussman, Ethan W.
Massachusetts Institute of Technology. Department of Mathematics
2023-07-31T19:45:07Z
2023-07-31T19:45:07Z
2023-06
2023-05-24T14:46:51.942Z
https://hdl.handle.net/1721.1/151508
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.
Ph.D.
Massachusetts Institute of Technology
In Copyright - Educational Use Permitted
Copyright retained by author(s)
https://rightsstatements.org/page/InC-EDU/1.0/
Scattering at threshold in massive wave propagation and ionization
Thesis
application/pdf
Doctoral
Doctor of Philosophy
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="dcbbc93e-75ee-4420-963a-36ca7320ef3b">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Title>Scattering at threshold in massive wave propagation and ionization</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2023-06</PublicationDate>
<Authors>
<Author>
<DisplayName>Sussman, Ethan W.</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>https://rightsstatements.org/page/InC-EDU/1.0/</License>
<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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>