A. V. Pereskokov, “Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters”, TMF, 178:1 (2014), 88–106; Theoret. and Math. Phys., 178:1 (2014), 76

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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 178, Number 1, Pages 88–106
DOI: https://doi.org/10.4213/tmf8561 (Mi tmf8561)

This article is cited in 12 scientific papers (total in 12 papers)

Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters

A. V. Pereskokov^ab

^a Moscow Power Engineering Institute, Moscow, Russia
^b Moscow Institute for Electronics and Mathematics, Higher School of Economics, Moscow, Russia

Full-text PDF (549 kB) Citations (12)

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DOI: https://doi.org/10.4213/tmf8561

Abstract: We consider the problem for eigenvalues of a perturbed two-dimensional oscillator in the case of a resonance frequency. The exciting potential is given by a Hartree-type integral operator with a smooth self-action potential. We find asymptotic eigenvalues and asymptotic eigenfunctions near the upper boundary of spectral clusters, which form around energy levels of the nonperturbed operator. To calculate them, we use asymptotic formulas for quantum means.

Keywords: self-consistent field, method of quantum averaging, coherent transformation, WKB approximation, spectral cluster, quantum mean.

Received: 09.06.2013

English version:
Theoretical and Mathematical Physics, 2014, Volume 178, Issue 1, Pages 76–92
DOI: https://doi.org/10.1007/s11232-014-0131-8

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: A. V. Pereskokov, “Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters”, TMF, 178:1 (2014), 88–106; Theoret. and Math. Phys., 178:1 (2014), 76–92

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https://www.mathnet.ru/eng/tmf/v178/i1/p88

This publication is cited in the following 12 articles:

A. A. Fedotov, “Complex WKB Method (One-Dimensional Linear Problems on the Complex Plane)”, Math Notes, 114:5-6 (2023), 1418
A. V. Pereskokov, “Semiclassical Asymptotics of the Spectrum of a Two-Dimensional Hartree Type Operator Near Boundaries of Spectral Clusters”, J Math Sci, 264:5 (2022), 617
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
A. V. Pereskokov, “Semiclassical asymptotic spectrum of the two-dimensional Hartree operator near a local maximum of the eigenvalues in a spectral cluste”, Theoret. and Math. Phys., 205:3 (2020), 1652–1665
D. A. Vakhrameeva, A. V. Pereskokov, “Asymptotics of the Spectrum and Quantum Averages of a Hartree Type Operator Near the Lower Boundaries of Spectral Clusters”, J Math Sci, 247:6 (2020), 820
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 Asymptotics of Solutions to Hartree Type Equations Concentrated on Segments”, J Math Sci, 226:4 (2017), 462
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
Pereskokov A., “Asymptotics of the Hartree-type operator spectrum near the lower boundaries of spectral clusters”, Appl. Anal., 95:7, SI (2016), 1560–1569
Alexander V. Pereskokov, 2016 Days on Diffraction (DD), 2016, 323
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

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

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