Scattering matrices for perturbations of Laplace operator by infinite sums of zero-range potentials
UDC 517.983, 517.984 We study the resolvents and scattering matrices for the following pairs of unbounded self-adjoint operators in $\mathbb{L}_{2}(\mathbf{R}_{3})$: the standard Laplace operator $A$ and its self-adjoint perturbation, which rigorously realizes the formal sum of $A$ with linear combi...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9170 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.983, 517.984
We study the resolvents and scattering matrices for the following pairs of unbounded self-adjoint operators in $\mathbb{L}_{2}(\mathbf{R}_{3})$: the standard Laplace operator $A$ and its self-adjoint perturbation, which rigorously realizes the formal sum of $A$ with linear combinations of infinitely many zero-range potentials. By using Krein’s resolvent formula for the perturbed operator, we establish sufficient conditions for the resolvent difference of the analyzed pair of operators to be a nuclear operator. Under these conditions, we deduce and analyze an explicit formula for the corresponding scattering matrices. |
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| DOI: | 10.3842/umzh.v78i7-8.9170 |