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PreprintarXiv licencearXiv

Solving Inverse Dirac-weighted Sturm-Liouville Problems via Cauchy problems

  • Min Zhao
  • Jiangang Qi
  • and Xiao Chen
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Abstract

Building on the point interaction method developed in our previous work, this paper studies inverse eigenvalue problems for regular Sturm-Liouville problems with Dirac weights. More precisely, we explicitly reconstruct the potential of regular Sturm-Liouville problems with the single-point and two-point Dirac weights from the solutions of a class of Cauchy problems which is completely determined by the first eigenvalues of a family of perturbed problems originating from moving point interaction models in quantum mechanics. Finally, the multi-point Dirac weighted case is also discussed.

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Cite

BibTeXRIS
BibTeX
@misc{zhao2026solving,
  title = {{Solving Inverse Dirac-weighted Sturm-Liouville Problems via Cauchy problems}},
  author = {Min Zhao and Jiangang Qi and and Xiao Chen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19715},
  eprint = {2609.19715},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19715},
}
RIS
TY  - UNPB
TI  - Solving Inverse Dirac-weighted Sturm-Liouville Problems via Cauchy problems
AU  - Min Zhao
AU  - Jiangang Qi
AU  - and Xiao Chen
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.19715
UR  - https://arxiv.org/abs/2609.19715
AB  - Building on the point interaction method developed in our previous work, this paper studies inverse eigenvalue problems for regular Sturm-Liouville problems with Dirac weights. More precisely, we explicitly reconstruct the potential of regular Sturm-Liouville problems with the single-point and two-point Dirac weights from the solutions of a class of Cauchy problems which is completely determined by the first eigenvalues of a family of perturbed problems originating from moving point interaction models in quantum mechanics. Finally, the multi-point Dirac weighted case is also discussed.
ER  -