V. V. Belov, F. N. Litvinets, A. Yu. Trifonov, “Semiclassical spectral series of a Hartree-type operator corresponding to a rest point of the classical Hamilton–Ehrenfest system”, TMF, 150:1 (2007), 26–40; Theoret. and Math. Phys., 150:1 (2007), 21

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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 150, Number 1, Pages 26–40
DOI: https://doi.org/10.4213/tmf5964 (Mi tmf5964)

This article is cited in 14 scientific papers (total in 14 papers)

Semiclassical spectral series of a Hartree-type operator corresponding to a rest point of the classical Hamilton–Ehrenfest system

V. V. Belov^a, F. N. Litvinets^b, A. Yu. Trifonov^b

^a Moscow State Institute of Electronics and Mathematics
^b Tomsk Polytechnic University

Full-text PDF (524 kB) Citations (14)

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DOI: https://doi.org/10.4213/tmf5964

Abstract: We consider the classical equations of motion in quantum means, i.e., the Hamilton–Ehrenfest system. In the semiclassical approximation in the framework of the covariant approach based on these equations, we construct the spectral series of a nonlinear Hartree-type operator corresponding to a rest point.

Keywords: complex germ method, spectral series, Hartree equation.

Received: 26.05.2006

English version:
Theoretical and Mathematical Physics, 2007, Volume 150, Issue 1, Pages 21–33
DOI: https://doi.org/10.1007/s11232-007-0003-6

Bibliographic databases:

Language: Russian

Citation: V. V. Belov, F. N. Litvinets, A. Yu. Trifonov, “Semiclassical spectral series of a Hartree-type operator corresponding to a rest point of the classical Hamilton–Ehrenfest system”, TMF, 150:1 (2007), 26–40; Theoret. and Math. Phys., 150:1 (2007), 21–33

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Linking options:

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This publication is cited in the following 14 articles:

A. V. Pereskokov, “Asymptotics of hypergeometric coherent states and eigenfunctions of the hydrogen atom in a magnetic field. Determination of self-consistent energy levels”, Theoret. and Math. Phys., 222:3 (2025), 453–470
Anton Kulagin, Alexander Shapovalov, “Quasiparticle solutions for the nonlocal NLSE with an anti-Hermitian term in semiclassical approximation”, Eur. Phys. J. Plus, 140:3 (2025)
A. V. Pereskokov, “Asymptotics of the spectrum of a Hartree-type operator with a screened Coulomb self-action potential near the upper boundaries of spectral clusters”, Theoret. and Math. Phys., 209:3 (2021), 1782–1797
D. A. Vakhrameeva, A. V. Pereskokov, “Asymptotics of the spectrum of a two-dimensional Hartree-type operator with a Coulomb self-action potential near the lower boundaries of spectral clusters”, Theoret. and Math. Phys., 199:3 (2019), 864–877
A. V. Pereskokov, “Semiclassical Asymptotics of the Spectrum near the Lower Boundary of Spectral Clusters for a Hartree-Type Operator”, Math. Notes, 101:6 (2017), 1009–1022
A. V. Pereskokov, “Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters”, Theoret. and Math. Phys., 187:1 (2016), 511–524
A. V. Pereskokov, “Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: Asymptotic solutions localized near a circle”, Theoret. and Math. Phys., 183:1 (2015), 516–526
A. V. Pereskokov, “Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters”, Theoret. and Math. Phys., 178:1 (2014), 76–92
Aleksandr L. Lisok, Aleksandr V. Shapovalov, Andrey Yu. Trifonov, “Symmetry and Intertwining Operators for the Nonlocal Gross–Pitaevskii Equation”, SIGMA, 9 (2013), 066, 21 pp.
Lipskaya A.V., Pereskokov A.V., “Asimptoticheskie resheniya odnomernogo uravneniya Khartri s negladkim potentsialom vzaimodeistviya. Asimptotika kvantovykh srednikh”, Vestn. Mosk. energeticheskogo in-ta, 2012, no. 6, 105–116
Belov V.V., Smirnova E.I., Trifonov A.Yu., “Semiclassical spectral series for the two-component Hartree-type equation”, Russian Phys. J., 54:6 (2011), 639–648
Litvinets F.N., “Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field”, J. Phys. A, 40:36 (2007), 11129
I. V. Khirnos, F. N. Litvinets, A. Yu. Trifonov, M. A. Shipulya, “Semiclassical spectral series of the two-component Hartree-type operator”, Russ Phys J, 50:5 (2007), 497
Belov V.V., “Semiclassical spectrum for a Hartree-type equation corresponding to a rest point of the Hamilton-Ehrenfest system”, J. Phys. A, 39:34 (2006), 10821

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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