Geodesic
An estimate for the number of eigenvalues of the Schr\"odinger operator with a~complex potential
Sbornik. Mathematics, Tome 208 (2017) no. 2, pp. 269-284

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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. 
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     author = {S. A. Stepin},
     title = {An estimate for the number of eigenvalues of the {Schr\"odinger} operator with a~complex potential},
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S. A. Stepin. An estimate for the number of eigenvalues of the Schr\"odinger operator with a~complex potential. Sbornik. Mathematics, Tome 208 (2017) no. 2, pp. 269-284. http://geodesic.mathdoc.fr/item/SM_2017_208_2_a5/