Abstract
By the Moutard transformation method we construct two-dimensional Schrödinger operators with real smooth potentials decaying at infinity and having a multiple positive eigenvalue. These potentials are rational functions of spatial variables and their sines and cosines.
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References
J. von Neumann and E. P. Wigner, Z. Phys., 30 (1929), 465–467.
T. Kato, Comm. Pure Appl. Math., 12 (1959), 403–425.
I. A. Taimanov and S. P. Tsarev, Uspekhi Mat. Nauk, 62:3 (2007), 217–218; English transl.: Russian Math. Surveys, 62:3 (2007), 631–633.
I. A. Taimanov and S. P. Tsarev, Teor. Mat. Fiz., 157:2 (2008), 188–207; English transl.: Theoret. Math. Phys., 157:2 (2008), 1525–1541.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 48, No. 4, pp. 74–77, 2014
Original Russian Text Copyright © by R. G. Novikov, I. A. Taimanov, and S. P. Tsarev
The work was partially supported by Federal Targeted Program No. 14.A18.21.0866 of the Ministry of Education and Science of Russian Federation (R. G. N.), the interdisciplinary project “Geometrical and algebraic methods for finding explicit solutions to equations of mathematical physics and continuum mechanics” of Russian Academy of Sciences, Siberian Branch (I. A. T. and S. P. Ts.), by grant 1431/GF of the Ministry of Education and Science of Republic of Kazakhstan (I. A. T.), and by the 2014 research government order No. 1.1462.2014/K of the Ministry of Education and Science for Siberian Federal University (S. P. Ts.).
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Novikov, R.G., Taimanov, I.A. & Tsarev, S.P. Two-dimensional von Neumann-Wigner potentials with a multiple positive eigenvalue. Funct Anal Its Appl 48, 295–297 (2014). https://doi.org/10.1007/s10688-014-0073-9
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DOI: https://doi.org/10.1007/s10688-014-0073-9