Abstract
Let us consider the scattering theory of one-dimensional Schrödinger equation defined by piecewise constant potentials with compact support. We construct the asymptotics of reflection coefficient by iterating the transition matrices. The jump points of the step potential appear in the asymptotics of reflection coefficient. Accordingly, we investigate the modulus of reflection coefficient. The modulus is connected to the zero set of reflection coefficient via Nevanlinna-Levin type of representation theorem. The growth theory of zero set of the reflection coefficient plays a role.
Key words: Schrödinger equation, piecewise constant potential, scattering
theory, Nevanlinna-Levin theorem
Full Text
Article Information
| Title | Reconstruction of Piecewise Constant Potential with Phaseless Reflection Coefficient |
| Source | Methods Funct. Anal. Topology, Vol. 32 (2026), no. 2, 116-128 |
| DOI | 10.31392/MFAT-npu26_2.2026.02 |
| Milestones | Received 17/07/2025; Revised 10/01/2026 |
| Copyright | The Author(s) 2026 (CC BY-SA) |
Authors Information
Lung-Hui Chen
General Education Center, Ming Chi University of Technology, Taishan Dist., New Taipei City, 24301, Taiwan
Citation Example
Lung-Hui Chen, Reconstruction of Piecewise Constant Potential with Phaseless Reflection Coefficient, Methods Funct. Anal. Topology 32
(2026), no. 2, 116-128.
BibTex
@article {MFAT2277,
AUTHOR = {Lung-Hui Chen},
TITLE = {Reconstruction of Piecewise Constant Potential with Phaseless Reflection Coefficient},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {32},
YEAR = {2026},
NUMBER = {2},
PAGES = {116-128},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_2.2026.02},
URL = {https://mfat.imath.kiev.ua/article/?id=2277},
}
