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).


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
Full Text: DOI


[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).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.