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Mat. Sb., 2017, Volume 208, Number 2, Pages 104–120 (Mi msb8686)  

An estimate for the number of eigenvalues of the Schrödinger operator with a complex potential

S. A. Stepin

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University

Abstract: For the Schrödinger operator whose potential is rapidly decreasing at infinity, an estimate for the number of eigenvalues is given, thus answering a question going back to Gelfand. The case of three-dimensional configuration space is chosen for simplicity of presentation; all the results formulated in the paper can be extended to an arbitrary number of degrees of freedom.
Bibliography: 19 titles.

Keywords: Schrödinger operator, Fredholm determinant, total multiplicity of eigenvalues.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00117-а
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 16-01-00117-a).


DOI: https://doi.org/10.4213/sm8686

Full text: PDF file (494 kB)
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English version:
Sbornik: Mathematics, 2017, 208:2, 269–284

Bibliographic databases:

Document Type: Article
UDC: 517.984.56
MSC: 35J10, 35P15
Received: 01.03.2016 and 24.10.2016

Citation: S. A. Stepin, “An estimate for the number of eigenvalues of the Schrödinger operator with a complex potential”, Mat. Sb., 208:2 (2017), 104–120; Sb. Math., 208:2 (2017), 269–284

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