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PreprintarXiv licencearXiv

Inverse spectral results for the magnetic Schrödinger operator in low dimensions

  • Devon Farrell
  • Anna Holloway
  • Nikhil Savale
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Abstract

We consider the semiclassical magnetic Schrödinger operator in dimensions one and two. The first result is that an even one dimensional semiclassical potential is spectrally determined by the Schrödinger operator. The second result states that a two dimensional radial magnetic field is spectrally determined by a purely magnetic Schrödinger operator. This extends the earlier work of Guillemin-Wang and answers a conjecture of theirs therein.

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Cite

BibTeXRIS
BibTeX
@misc{farrell2026inverse,
  title = {{Inverse spectral results for the magnetic Schrödinger operator in low dimensions}},
  author = {Devon Farrell and Anna Holloway and Nikhil Savale},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01479},
  eprint = {2610.01479},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01479},
}
RIS
TY  - UNPB
TI  - Inverse spectral results for the magnetic Schrödinger operator in low dimensions
AU  - Devon Farrell
AU  - Anna Holloway
AU  - Nikhil Savale
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01479
UR  - https://arxiv.org/abs/2610.01479
AB  - We consider the semiclassical magnetic Schrödinger operator in dimensions one and two. The first result is that an even one dimensional semiclassical potential is spectrally determined by the Schrödinger operator. The second result states that a two dimensional radial magnetic field is spectrally determined by a purely magnetic Schrödinger operator. This extends the earlier work of Guillemin-Wang and answers a conjecture of theirs therein.
ER  -