Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
On eigenvalues of the Schrödinger operator with a complex-valued polynomial potential
Stockholm University, Faculty of Science, Department of Mathematics.
2010 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, we generalize a recent result of A. Eremenko and A. Gabrielov on irreducibility of the spectral discriminant for the Schroedinger equation with quartic potentials.

In the first paper, we consider the eigenvalue problem with a complex-valued polynomial potential of arbitrary degree d and show that the spectral determinant of this problem is connected and irreducible. In other words, every eigenvalue can be reached from any other by analytic continuation. We also prove connectedness of the parameter spaces of the potentials that admit eigenfunctions satisfying k > 2 boundary conditions, except for the case d is even and k = d/2. In the latter case, connected components of the parameter space are distinguished by the number of zeros of the eigenfunctions.

In the second paper, we only consider even polynomial potentials, and show that the spectral determinant for the eigenvalue problem consists of two irreducible components. A similar result to that of paper I is proved for k boundary conditions.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics , 2010. , p. 51
Series
Research Reports in Mathematics, ISSN 1401-5617 ; 5
Keywords [en]
schroedinger, even spectral determinant polynomial potential eigenvalue
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-52064OAI: oai:DiVA.org:su-52064DiVA, id: diva2:386585
Presentation
2010-12-14, Rum 306, Hus 5, Matematiska institutionen, Kräftriket, Stockholms universitet, Stockholm, 21:48 (English)
Opponent
Supervisors
Available from: 2011-01-27 Created: 2011-01-12 Last updated: 2022-02-24Bibliographically approved

Open Access in DiVA

fulltext(507 kB)593 downloads
File information
File name FULLTEXT01.pdfFile size 507 kBChecksum SHA-512
cbb94d5efcb0d98333d47d673eb2dc8c082be07ffa61de66cb7487c2fac7fb5501aa1e40a291cffa191e625aeb2cb8545b708a3adb98ce0a72fa0c217f80a1f4
Type fulltextMimetype application/pdf

Other links

http://www2.math.su.se/reports/2010/5

Authority records

Alexandersson, Per

Search in DiVA

By author/editor
Alexandersson, Per
By organisation
Department of Mathematics
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar
Total: 594 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 674 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf