Solutions of the Lippmann-Schwinger equation for confocal parabolic billiards
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914712587862016 |
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| author | Ruiz-Biestro, Alberto Gutierrez-Vega, Julio C. |
| author_facet | Ruiz-Biestro, Alberto Gutierrez-Vega, Julio C. |
| contents | We present analytical and numerical solutions of the Lippmann-Schwinger equation for the scattered wavefunctions generated by confocal parabolic billiards and parabolic segments with various $δ$-type potential-strength functions. The analytical expressions are expressed as summations of products of parabolic cylinder functions $D_m$. We numerically investigate the resonances and tunneling in the confocal parabolic billiards by employing an accurate boundary wall method that provides a complete inside-outside picture. The criterion for discretizing the parabolic sides of the billiard is explained in detail. We discuss the phenomenon of transparency at certain eigenenergies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07396 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Solutions of the Lippmann-Schwinger equation for confocal parabolic billiards Ruiz-Biestro, Alberto Gutierrez-Vega, Julio C. Quantum Physics Computational Physics Optics We present analytical and numerical solutions of the Lippmann-Schwinger equation for the scattered wavefunctions generated by confocal parabolic billiards and parabolic segments with various $δ$-type potential-strength functions. The analytical expressions are expressed as summations of products of parabolic cylinder functions $D_m$. We numerically investigate the resonances and tunneling in the confocal parabolic billiards by employing an accurate boundary wall method that provides a complete inside-outside picture. The criterion for discretizing the parabolic sides of the billiard is explained in detail. We discuss the phenomenon of transparency at certain eigenenergies. |
| title | Solutions of the Lippmann-Schwinger equation for confocal parabolic billiards |
| topic | Quantum Physics Computational Physics Optics |
| url | https://arxiv.org/abs/2312.07396 |