Geodesic
Quantum-mechanical oscillator with arbitrary anharmonicity: $1/N$ Expansion and perturbation theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 56 (1983) no. 3, pp. 357-367 
A. V. Kudinov; M. A. Smondyrev. Quantum-mechanical oscillator with arbitrary anharmonicity: $1/N$ Expansion and perturbation theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 56 (1983) no. 3, pp. 357-367. http://geodesic.mathdoc.fr/item/TMF_1983_56_3_a3/
@article{TMF_1983_56_3_a3,
     author = {A. V. Kudinov and M. A. Smondyrev},
     title = {Quantum-mechanical oscillator with arbitrary anharmonicity: $1/N${~Expansion} and perturbation theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {357--367},
     year = {1983},
     volume = {56},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_56_3_a3/}
}
TY  - JOUR
AU  - A. V. Kudinov
AU  - M. A. Smondyrev
TI  - Quantum-mechanical oscillator with arbitrary anharmonicity: $1/N$ Expansion and perturbation theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1983
SP  - 357
EP  - 367
VL  - 56
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1983_56_3_a3/
LA  - ru
ID  - TMF_1983_56_3_a3
ER  - 
%0 Journal Article
%A A. V. Kudinov
%A M. A. Smondyrev
%T Quantum-mechanical oscillator with arbitrary anharmonicity: $1/N$ Expansion and perturbation theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1983
%P 357-367
%V 56
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1983_56_3_a3/
%G ru
%F TMF_1983_56_3_a3

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

The properties of the $1/N$ expansion are investigated for the problem of an Ndimensional anharmonic oscillator with arbitrary power anharmonieity. The first six terms in the expansion of the energies of the ground and first excited levels are obtained in analytic form. The asymptotic behavior of the coefficients in large orders of the $1/N$ expansion is investigated. The obtained formulas are used to determine expressions for the first six coefficients of the standard perturbation theory in powers of the coupling constant in the case of an $N$-dimensional potential with two degenerate minima. The asymptotic behavior of these coefficients at high orders of perturbation theory is discussed.

[1] Hioe F. T., McMillan D., Montroll E. W., Phys. Rep., 43:7 (1978), 305–335 ; Zinn-Justin J., Phys. Rep., 70:2 (1981), 109–167 ; Simon B., Int. J. Quantum Chem., 21:1 (1982), 3–25 | DOI | MR | DOI | MR | DOI

[2] Dolgov A. D., Eletskii V. L., Popov V. S., Angarmonicheskii ostsillyator: teoriya vozmuschenii, kvaziklassika, metod Pade, Preprint ITEF-72, ITEF, M., 1979 | MR

[3] Dolgov A. D., Popov V. S., ZhETF, 75 (1978), 2010–2026

[4] Brezin E., Le Guillou J. C., Zinn-Justin J., Phys. Rev., D15:6 (1977), 1544–1564 | MR

[5] Brezin E., Parisi G., Zinn-Justin J., Phys. Rev., D16:2 (1977), 408–412

[6] Ferrell R. A., Scalapino D. J., Phys. Rev., A9:2 (1974), 846–867 | DOI

[7] Brezin E., Hikami S., J. Phys., A12:6 (1979), 759–770

[8] Koudinov A. V., Smondyrev M. A., Czech. J. Phys., B32:5 (1982), 556–564 | DOI

[9] Mlodinow L. D., Papanicolaou, Ann. Phys., 128:2 (1980), 314–334 | DOI | MR

[10] Koudinov A. V., Smondyrev M. A., Quantum-mechanical oscillator with arbitrary anharmonicity: $1/N$-expansion and perturbation theory, Preprint E2-82-705, JINR, Dubna, 1982 | MR

[11] Zinn-Justin J., J. Math. Phys., 22:3 (1981), 511–520 | DOI | MR

[12] Avron J., Seiller R., Phys. Rev., D23:6 (1981), 1316–1320 | MR

[13] Bender C. M. et al., Phys. Rev., D19:6 (1979), 1865–1881