Lippmann-Schwinger-Lanczos approach for inverse scattering problem of Schrodinger equation in the resonance frequency domain
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909568542441472 |
|---|---|
| author | Abilgazy, Anarzhan Zaslavskiy, Mikhail |
| author_facet | Abilgazy, Anarzhan Zaslavskiy, Mikhail |
| contents | Reconstructions of potential in Schrodinger equation with data in the diffusion frequency domain have been successfully obtained within Lippmann-Schwinger-Lanczos (LSL) approach, however limited resolution away from the sensor positions resulted in rather blurry images. To improve the reconstructions, in this work we extended the applicability of the approach to the data in the resonance frequency domain. We proposed a specific data sampling according to Weyl's law that allows us to obtain sharp images without oversampling and overwhelming computational complexity. Numerical results presented at the end illustrate the performance of the algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lippmann-Schwinger-Lanczos approach for inverse scattering problem of Schrodinger equation in the resonance frequency domain Abilgazy, Anarzhan Zaslavskiy, Mikhail Numerical Analysis Reconstructions of potential in Schrodinger equation with data in the diffusion frequency domain have been successfully obtained within Lippmann-Schwinger-Lanczos (LSL) approach, however limited resolution away from the sensor positions resulted in rather blurry images. To improve the reconstructions, in this work we extended the applicability of the approach to the data in the resonance frequency domain. We proposed a specific data sampling according to Weyl's law that allows us to obtain sharp images without oversampling and overwhelming computational complexity. Numerical results presented at the end illustrate the performance of the algorithm. |
| title | Lippmann-Schwinger-Lanczos approach for inverse scattering problem of Schrodinger equation in the resonance frequency domain |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.04607 |