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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.08497 |
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| _version_ | 1866908286121410560 |
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| author | Hörmann, Günther Oparnica, Ljubica Spreitzer, Christian |
| author_facet | Hörmann, Günther Oparnica, Ljubica Spreitzer, Christian |
| contents | We discuss spectral properties of a regularization approach to a Schrödinger equation set-up for the diffraction of a quantum particle at almost planar patterns. Physically meaningful initial values and potentials are modeled in terms of regularizing families and the solutions can be interpreted as generalized functions. We establish spectral and scattering theoretical properties of the regularizing solution families and provide some comparison with the more direct approximations and simplifications used in physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08497 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Modeling Schrödinger equation diffraction with generalized function potentials and initial values Hörmann, Günther Oparnica, Ljubica Spreitzer, Christian Mathematical Physics 81Q05, 35P25, 46F30 We discuss spectral properties of a regularization approach to a Schrödinger equation set-up for the diffraction of a quantum particle at almost planar patterns. Physically meaningful initial values and potentials are modeled in terms of regularizing families and the solutions can be interpreted as generalized functions. We establish spectral and scattering theoretical properties of the regularizing solution families and provide some comparison with the more direct approximations and simplifications used in physics. |
| title | Modeling Schrödinger equation diffraction with generalized function potentials and initial values |
| topic | Mathematical Physics 81Q05, 35P25, 46F30 |
| url | https://arxiv.org/abs/2212.08497 |