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Matematicheskie Zametki, 2024, Volume 116, Issue 6, Pages 969–981 (Mi mzm14457)  

Spectral Series of the Schrödinger Operator with Double Delta Potential on Two- and Three-Dimensional Surfaces of Revolution

V. V. Rykhlovab, A. I. Shafarevichabc

a Lomonosov Moscow State University
b Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
References:
Abstract: This article is devoted to the construction of spectral series of the Schrödinger operator with double delta potential of the form $H = -\frac{h^2}{2}\Delta + \delta_{x_1}(x) + \delta_{x_2}(x)$, $x\in M$, where $x_j$ are the poles of 2- or 3-surface of revolution $M$, in the semiclassical limit as $h\to 0$, and the operator is considered to be an arbitrary self-adjoint extension of the Laplace–Beltrami operator.
Keywords: Schrödinger operator, semiclassical asymptotics, delta potential, spectral problems.
Funding agency Grant number
Russian Science Foundation 22-11-00272
Received: 19.07.2024
Document Type: Article
UDC: 514.763.85
Language: Russian
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