Dispersive estimates for Schrödinger operators with negative Coulomb-like potentials in one dimension
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866912992182927360 |
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| author | Hoshiya, Akitoshi Taira, Kouichi |
| author_facet | Hoshiya, Akitoshi Taira, Kouichi |
| contents | In this paper, we consider the dispersive estimates for Schrödinger operators with Coulomb-like decaying potentials, such as $V(x)=-c|x|^{-μ}$ for $|x|\gg 1$ with $0<μ<2$, in one dimension. As an application, we establish both the standard and orthonormal Strichartz estimates for this model. One of the difficulties here is that perturbation arguments, which are typically applicable to rapidly decaying potentials, are not available. To overcome this, we derive a WKB expression for the spectral density and use a variant of the degenerate stationary phase formula to exploit its oscillatory behavior in the low-energy regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29731 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dispersive estimates for Schrödinger operators with negative Coulomb-like potentials in one dimension Hoshiya, Akitoshi Taira, Kouichi Analysis of PDEs Mathematical Physics 35J10, 35Q41, 34E20, 34E05 In this paper, we consider the dispersive estimates for Schrödinger operators with Coulomb-like decaying potentials, such as $V(x)=-c|x|^{-μ}$ for $|x|\gg 1$ with $0<μ<2$, in one dimension. As an application, we establish both the standard and orthonormal Strichartz estimates for this model. One of the difficulties here is that perturbation arguments, which are typically applicable to rapidly decaying potentials, are not available. To overcome this, we derive a WKB expression for the spectral density and use a variant of the degenerate stationary phase formula to exploit its oscillatory behavior in the low-energy regime. |
| title | Dispersive estimates for Schrödinger operators with negative Coulomb-like potentials in one dimension |
| topic | Analysis of PDEs Mathematical Physics 35J10, 35Q41, 34E20, 34E05 |
| url | https://arxiv.org/abs/2603.29731 |