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Quasiclassical soliton solutions of the Hartree equation. Newtonian interaction with screening. (English. Russian original) Zbl 1138.81416

Theor. Math. Phys. 40, No. 2, 715-721 (1980); translation from Teor. Mat. Fiz. 40, No. 2, 235-244 (1979).
Summary: A quasiclassical series of eigenvalues and spherically symmetric eigenfunctions is constructed for the translationally invariant Hartree equation in the case of the Newtonian interaction with screening (Yukawa potential).

MSC:

81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q51 Soliton equations
35Q40 PDEs in connection with quantum mechanics
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References:

[1] E. H. Lieb and B. Simon, Commun. Math. Phys.,53, 185 (1977). · doi:10.1007/BF01609845
[2] J. M. Chadam and R. T. Glassey, J. Math. Phys.,16, 1122 (1975). · Zbl 0299.35084 · doi:10.1063/1.522642
[3] V. P. Maslov, Complex Markov Chains and Feynman Path Integrals [in Russian], Nauka (1976). · Zbl 0449.35086
[4] V. P. Maslov, in: Modern Problems of Mathematics [in Russian], VINITI, Vol. 11 (1978), p. 153.
[5] M. V. Karasev and V. P. Maslov, in: Modern Problems of Mathematics [in Russian], VINITI, Vol. 13 (1979), p. 145.
[6] N. S. Zinchenko, Course of Lectures on Electron Optics [in Russian], State University, Khar’kov (1958).
[7] V. P. Maslov, Perturbation Theory and Asymptotic Methods [in Russian], MGU (1965).
[8] L. V. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis [in Russian], Fizmatgiz (1962). · Zbl 0083.35301
[9] N. N. Bogolyubov and K. P. Gurov, Zh. Eksp. Teor. Fiz.,17, 714 (1947).
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