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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.20229 |
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| _version_ | 1866913857094549504 |
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| author | Linde, Helmut |
| author_facet | Linde, Helmut |
| contents | Consider a closed curve of length $2π$ with curvature $κ(s)$ and the Schrödinger operator $H$ with $κ^2$ as the potential term. Let $λ_Γ$ be the lowest eigenvalue of $H$. The Ovals Conjecture proposed by Benguria and Loss states that $λ_Γ\ge 1$. While the conjecture remains open, the present work establishes a new lower bound of $0.81$ on $λ_Γ$, improving on the previously best known estimate of $0.6085$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20229 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An improved bound for the ground state of a Schrödinger operator on a loop Linde, Helmut Mathematical Physics Consider a closed curve of length $2π$ with curvature $κ(s)$ and the Schrödinger operator $H$ with $κ^2$ as the potential term. Let $λ_Γ$ be the lowest eigenvalue of $H$. The Ovals Conjecture proposed by Benguria and Loss states that $λ_Γ\ge 1$. While the conjecture remains open, the present work establishes a new lower bound of $0.81$ on $λ_Γ$, improving on the previously best known estimate of $0.6085$. |
| title | An improved bound for the ground state of a Schrödinger operator on a loop |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2504.20229 |