Geodesic
On the spectrum of the two-particle Schr\"odinger operator with point potential: one dimensional case
Nanosistemy: fizika, himiâ, matematika, Tome 14 (2023) no. 5, pp. 505-510

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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. 
@article{NANO_2023_14_5_a0,
     author = {Utkir N. Kuljanov},
     title = {On the spectrum of the two-particle {Schr\"odinger} operator with point potential: one dimensional case},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {505--510},
     publisher = {mathdoc},
     volume = {14},
     number = {5},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2023_14_5_a0/}
}
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Utkir N. Kuljanov. On the spectrum of the two-particle Schr\"odinger operator with point potential: one dimensional case. Nanosistemy: fizika, himiâ, matematika, Tome 14 (2023) no. 5, pp. 505-510. http://geodesic.mathdoc.fr/item/NANO_2023_14_5_a0/