Geodesic
Semiclassical Asymptotics of the Spectrum near the Lower Boundary of Spectral Clusters for a Hartree-Type Operator
Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 894-910

Voir la notice de l'article provenant de la source Math-Net.Ru

The eigenvalue problem for a perturbed two-dimensional resonant oscillator is considered. The exciting potential is given by a nonlocal nonlinearity of Hartree type with smooth self-action potential. To each representation of the rotation algebra corresponds the spectral cluster around an energy level of the unperturbed operator. Asymptotic eigenvalues and asymptotic eigenfunctions close to the lower boundary of spectral clusters are obtained. For their calculation, asymptotic formulas for quantum means are used.
Keywords: self-consistent field, spectral cluster, quantum averaging method, coherent transformation, the WKB approximation, turning point. 
@article{MZM_2017_101_6_a9,
     author = {A. V. Pereskokov},
     title = {Semiclassical {Asymptotics} of the {Spectrum} near the {Lower} {Boundary} of {Spectral} {Clusters} for a {Hartree-Type} {Operator}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {894--910},
     publisher = {mathdoc},
     volume = {101},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a9/}
}
TY  - JOUR
AU  - A. V. Pereskokov
TI  - Semiclassical Asymptotics of the Spectrum near the Lower Boundary of Spectral Clusters for a Hartree-Type Operator
JO  - Matematičeskie zametki
PY  - 2017
SP  - 894
EP  - 910
VL  - 101
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a9/
LA  - ru
ID  - MZM_2017_101_6_a9
ER  - 
%0 Journal Article
%A A. V. Pereskokov
%T Semiclassical Asymptotics of the Spectrum near the Lower Boundary of Spectral Clusters for a Hartree-Type Operator
%J Matematičeskie zametki
%D 2017
%P 894-910
%V 101
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a9/
%G ru
%F MZM_2017_101_6_a9
A. V. Pereskokov. Semiclassical Asymptotics of the Spectrum near the Lower Boundary of Spectral Clusters for a Hartree-Type Operator. Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 894-910. http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a9/