Eigenvalues of the discrete Schrödinger operator in the large coupling constant limit
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917924963352576 |
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| author | Gao, Siyu |
| author_facet | Gao, Siyu |
| contents | Let $(λ_-,λ_+)$ be a spectral gap of a periodic Schrödinger operator $A$ on the lattice ${\mathbb Z}^d$. Consider the operator $A(α)=A-αV$ where $V$ is a decaying positive potential on ${\mathbb Z}^d$. We study the asymptotic behavior of the number of eigenvalues of $A(t)$ passing through a point $λ\in (λ_-,λ_+)$ as $t$ grows from $0$ to $α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11257 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eigenvalues of the discrete Schrödinger operator in the large coupling constant limit Gao, Siyu Spectral Theory Let $(λ_-,λ_+)$ be a spectral gap of a periodic Schrödinger operator $A$ on the lattice ${\mathbb Z}^d$. Consider the operator $A(α)=A-αV$ where $V$ is a decaying positive potential on ${\mathbb Z}^d$. We study the asymptotic behavior of the number of eigenvalues of $A(t)$ passing through a point $λ\in (λ_-,λ_+)$ as $t$ grows from $0$ to $α$. |
| title | Eigenvalues of the discrete Schrödinger operator in the large coupling constant limit |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2502.11257 |