ON THE SPECTRUM OF THE TWO-PARTICLE SCHRÖDINGER OPERATOR WITH POINT POTENTIAL: ONE DIMENTIONAL CASE
2021 ◽
Vol 10
(12)
◽
pp. 3569-3578
Keyword(s):
In the paper a one-dimensional two-particle quantum system interacted by two identical point interactions is considered. The corresponding Schr\"{o}\-dinger 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 to the study of the operator $h_\varepsilon.$ First the essential spectrum is described. The existence of unique negative eigenvalue of the Schr\"{o}dinger operator is proved. Further, this eigenvalue and corresponding eigenfunction are found.
2020 ◽
Vol 54
(2)
◽
pp. 145-148
Keyword(s):
2018 ◽
Vol 42
(15)
◽
pp. 5072-5093
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1996 ◽
Vol 30
(2)
◽
pp. 144-146
◽
Keyword(s):
2006 ◽
Vol 40
(2)
◽
pp. 143-147
◽
Keyword(s):