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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.15536 |
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| _version_ | 1866913306476806144 |
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| author | Kato, Keiichi Nakahashi, Wataru Tadano, Yukihide |
| author_facet | Kato, Keiichi Nakahashi, Wataru Tadano, Yukihide |
| contents | We study non-smoothness of the fundamental solution for the Schrödinger equation with a spherically symmetric and super-quadratic potential in the sence that $V(x)\geq C|x|^{2+\varepsilon}$ at infinity with constants $C>0 $ and $\varepsilon>0$. More precisely, we show the fundamental solution $E(t,x,y)$ does not belong to $C^{1}$ as a function of $(t,x,y)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15536 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-smoothness of the fundamental solutions for Schrödinger equations with super-quadratic and spherically symmetric potential Kato, Keiichi Nakahashi, Wataru Tadano, Yukihide Analysis of PDEs Mathematical Physics 35J10 We study non-smoothness of the fundamental solution for the Schrödinger equation with a spherically symmetric and super-quadratic potential in the sence that $V(x)\geq C|x|^{2+\varepsilon}$ at infinity with constants $C>0 $ and $\varepsilon>0$. More precisely, we show the fundamental solution $E(t,x,y)$ does not belong to $C^{1}$ as a function of $(t,x,y)$. |
| title | Non-smoothness of the fundamental solutions for Schrödinger equations with super-quadratic and spherically symmetric potential |
| topic | Analysis of PDEs Mathematical Physics 35J10 |
| url | https://arxiv.org/abs/2310.15536 |