<div class="csl-bib-body">
<div class="csl-entry">Heitzinger, T. (2018). <i>Complex scaling for one-dimensional resonance problems in inhomogeneous exterior domains</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2018.58182</div>
</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2018.58182
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/5393
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dc.description.abstract
In this thesis the one-dimensional complex scaling method for generalized scaling profiles is introduced and applied to equations of Helmholtz-type with well known solutions in the exterior domain. We discuss the meaning of radiating solutions, prove conditions for the existence of unique radiating solutions to scattering problems, and show that solutions to scaled and unscaled problems are equivalent in some sense. We transfer most of these results to the time-independent Schrödinger equation with quadratically decaying potential functions. Potential functions of this type are non-trivial in the exterior domain and lead to solutions with inexplicit asymptotic behavior. We analyze the discrete spectrum of the associated Hamilton operator and test its dependence on the parameter a as well as the influence of discretization parameters. The method is implemented with the finite element software NGSolve.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
complex scaling
en
dc.subject
resonance problems
en
dc.title
Complex scaling for one-dimensional resonance problems in inhomogeneous exterior domains
en
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2018.58182
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Thomas Heitzinger
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dc.publisher.place
Wien
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E101 - Institut für Analysis und Scientific Computing
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dc.type.qualificationlevel
Diploma
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dc.identifier.libraryid
AC15152288
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dc.description.numberOfPages
52
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dc.identifier.urn
urn:nbn:at:at-ubtuw:1-115503
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dc.thesistype
Diplomarbeit
de
dc.thesistype
Diploma Thesis
en
tuw.author.orcid
0000-0002-3129-5054
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dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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item.fulltext
with Fulltext
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item.cerifentitytype
Publications
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item.mimetype
application/pdf
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item.openairecristype
http://purl.org/coar/resource_type/c_bdcc
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item.languageiso639-1
en
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item.openaccessfulltext
Open Access
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item.openairetype
master thesis
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item.grantfulltext
open
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crisitem.author.dept
E193-01 - Forschungsbereich Computer Vision
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crisitem.author.orcid
0000-0002-3129-5054
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crisitem.author.parentorg
E193 - Institut für Visual Computing and Human-Centered Technology