Transparent boundary conditions for the stationary Schroedinger equation via Weyl-Titchmarsh theory
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912072213725184 |
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| author | Derkach, V. A. Trunk, C. Yusupov, J. R. Matrasulov, D. U. |
| author_facet | Derkach, V. A. Trunk, C. Yusupov, J. R. Matrasulov, D. U. |
| contents | We propose a general approach for deriving transparent boundary conditions for the stationary Schroedinger equation with arbitrary potential. It is proven that the transparent boundary conditions 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 Schroedinger equation with the harmonic potential and the Poeschl-Teller potential are considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10232 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transparent boundary conditions for the stationary Schroedinger equation via Weyl-Titchmarsh theory Derkach, V. A. Trunk, C. Yusupov, J. R. Matrasulov, D. U. Mathematical Physics Mesoscale and Nanoscale Physics Quantum Physics We propose a general approach for deriving transparent boundary conditions for the stationary Schroedinger equation with arbitrary potential. It is proven that the transparent boundary conditions 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 Schroedinger equation with the harmonic potential and the Poeschl-Teller potential are considered. |
| title | Transparent boundary conditions for the stationary Schroedinger equation via Weyl-Titchmarsh theory |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2410.10232 |