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MATHEMATICS
On the spectrum of the two-particle Schrödinger operator with point potential: one dimensional case
Utkir N. Kuljanov Samarkand State University, Samarkand, Uzbekistan
Abstract:
In the paper, a one-dimensional two-particle quantum system interacted by two identical point interactions is considered. The corresponding Schrödinger operator (energy operator) $h_\varepsilon$ depending on $\varepsilon$ is constructed as a self-adjoint extension of the symmetric Laplace operator. The main results of the work are based on the study of the operator $h_\varepsilon$. First, the essential spectrum is described. The existence of unique negative eigenvalue of the Schrödinger operator is proved. Further, this eigenvalue and the corresponding eigenfunction are found.
Keywords:
two-particle quantum system, symmetric Laplace operator, eigenvalue, eigenfunction, energy operator.
Received: 19.08.2022 Revised: 18.09.2023 Accepted: 19.09.2023
Citation:
Utkir N. Kuljanov, “On the spectrum of the two-particle Schrödinger operator with point potential: one dimensional case”, Nanosystems: Physics, Chemistry, Mathematics, 14:5 (2023), 505–510
Linking options:
https://www.mathnet.ru/eng/nano1215 https://www.mathnet.ru/eng/nano/v14/i5/p505
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Abstract page: | 39 | Full-text PDF : | 31 |
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