On the spectrum of the two-particle Schrödinger operator with point potential: one dimensional case
https://doi.org/10.17586/2220-8054-2023-14-5-505-510
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" depending on " 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". First, the essential spectrum is described. The existence of unique negative eigenvalue of the Schr¨odinger operator is proved. Further, this eigenvalue and the corresponding eigenfunction are found.
About the Author
U. N. Kuljanov
Samarkand State University; Samarkand branch of Tashkent State University of Economics
Uzbekistan
Uzbekistan
Utkir Nematovich Kuljanov
140104, University boulvare. 15, Samarkand
Professorlar street 51, Samarkand
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Review
For citations:
Kuljanov U.N. On the spectrum of the two-particle Schrödinger operator with point potential: one dimensional case. Nanosystems: Physics, Chemistry, Mathematics. 2023;14(5):505-510. https://doi.org/10.17586/2220-8054-2023-14-5-505-510
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