Revisiting the Weak Coupling Phenomenon for Two-Dimensional Schrödinger Operators
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| Format: | Preprint |
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2026
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| _version_ | 1866917425672355840 |
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| author | Behrndt, Jussi Siegl, Petr Weber, Nicolas |
| author_facet | Behrndt, Jussi Siegl, Petr Weber, Nicolas |
| contents | We study the existence of negative eigenvalues for two-dimensional Schrödinger operators with real-valued potentials in the weak coupling regime. In his pioneering paper [Simon 1976] from half a century ago, Simon was the first to describe the unique negative eigenvalue emerging from the threshold of the essential spectrum of one- and two-dimensional Schrödinger operators. The aim of this paper is to extend Simon's results in two dimensions to a broader class of potentials, allowing for both stronger singularities and slower decay at infinity, at the cost of losing uniqueness of weakly coupled eigenvalues. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_19284 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Revisiting the Weak Coupling Phenomenon for Two-Dimensional Schrödinger Operators Behrndt, Jussi Siegl, Petr Weber, Nicolas Spectral Theory Analysis of PDEs Primary 81Q10, 35J10, Secondary 47A55, 47A75 We study the existence of negative eigenvalues for two-dimensional Schrödinger operators with real-valued potentials in the weak coupling regime. In his pioneering paper [Simon 1976] from half a century ago, Simon was the first to describe the unique negative eigenvalue emerging from the threshold of the essential spectrum of one- and two-dimensional Schrödinger operators. The aim of this paper is to extend Simon's results in two dimensions to a broader class of potentials, allowing for both stronger singularities and slower decay at infinity, at the cost of losing uniqueness of weakly coupled eigenvalues. |
| title | Revisiting the Weak Coupling Phenomenon for Two-Dimensional Schrödinger Operators |
| topic | Spectral Theory Analysis of PDEs Primary 81Q10, 35J10, Secondary 47A55, 47A75 |
| url | https://arxiv.org/abs/2604.19284 |