Transparent boundary conditions for the stationary Schrödinger equation via Weyl–Titchmarsh theory<sup>*</sup>
Abstract We propose a general approach for deriving transparent boundary conditions (TBCs) for the stationary Schrödinger equation with arbitrary potential. It is proven that the TBCs can be written in terms of the Weyl–Titchmarsh coefficients. As examples for the application of the proposed approach, two special cases for the stationary Schrödinger equation with the harmonic potential and the Pöschl–Teller potential are considered.
Authors
- Carsten Trunk (ORCID: https://orcid.org/0000-0003-3023-5567)
- Jambul Yusupov (ORCID: https://orcid.org/0000-0003-1758-6805)
- D. U. Matrasulov (ORCID: https://orcid.org/0000-0001-8957-0058)
- Volodymyr Derkach (ORCID: https://orcid.org/0000-0003-0343-232X)
Institutions
- Technische Universität Ilmenau (DE)
- Turin Polytechnic University (UZ)
- Westminster International University in Tashkent (UZ)
Publication Details
- Journal
- Journal of Physics A Mathematical and Theoretical
- Published
- 2025-08-04
- DOI
- https://doi.org/10.1088/1751-8121/adf787
- Citations
- 12
- Primary Topic
- Topological Materials and Phenomena
- Type
- article
- Field-Weighted Citation Impact
- 14.96
Funders
- H2020 Marie Skłodowska-Curie Actions