Geodesic
Splitting amplitudes of the lowest energy levels of the Schrödinger operator with double-well potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 3, pp. 426-434 
S. Yu. Dobrokhotov; V. N. Kolokoltsov. Splitting amplitudes of the lowest energy levels of the Schrödinger operator with double-well potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 3, pp. 426-434. http://geodesic.mathdoc.fr/item/TMF_1993_94_3_a7/
@article{TMF_1993_94_3_a7,
     author = {S. Yu. Dobrokhotov and V. N. Kolokoltsov},
     title = {Splitting amplitudes of the lowest energy levels of the {Schr\"odinger} operator with double-well potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {426--434},
     year = {1993},
     volume = {94},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_94_3_a7/}
}
TY  - JOUR
AU  - S. Yu. Dobrokhotov
AU  - V. N. Kolokoltsov
TI  - Splitting amplitudes of the lowest energy levels of the Schrödinger operator with double-well potential
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1993
SP  - 426
EP  - 434
VL  - 94
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1993_94_3_a7/
LA  - ru
ID  - TMF_1993_94_3_a7
ER  - 
%0 Journal Article
%A S. Yu. Dobrokhotov
%A V. N. Kolokoltsov
%T Splitting amplitudes of the lowest energy levels of the Schrödinger operator with double-well potential
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1993
%P 426-434
%V 94
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1993_94_3_a7/
%G ru
%F TMF_1993_94_3_a7

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

An analytic method is proposed for calculating the asymptotic splitting of the lowest energy levels of the Schrödinger operator with a symmetric double-well potential. The potential describing a chain of pairwise interacting quantum particles in a common double-well potential is considered as an example. The limit of a large number of particles is investigated.

[1] Maslov V. P., Kompleksnyi metod VKB v nelineinykh uravneniyakh, Nauka, M., 1977 | MR

[2] Polyakov A. M., Nucl. Phys. B, 120 (1977), 429–456 | DOI | MR

[3] Radzharaman R., Solitony i instantony v kvantovoi teorii polya, Mir, M., 1983 | MR

[4] Maslov V. P., Trudy MIAN, 163, 1984, 150–180 | MR | Zbl

[5] Pankratova T. F., DAN SSSR, 276:4 (1984), 795–799 | MR | Zbl

[6] Dobrokhotov S. Yu., Kolokoltsov V. N., Maslov V. P., TMF, 87:3 (1991), 323–375 ; Dobrokhotov S. Yu., Kolokoltsov V. N., Maslov V. P., Adv. Soviet Math., 13, Amer. Math. Soc., Providence, RI, 1992, 1–46 | MR | Zbl | MR

[7] Simon B., Ann. Inst. H. Poincarè, 38 (1983), 295–307 | MR

[8] Simon B., Ann. of Math., 120 (1984), 89–118 | DOI | MR | Zbl

[9] Coleman S., The Whys of Subnuclear Physics, 1979, no. 4, 805–916 | DOI

[10] Helffer B., Sjostrand J., Ann. Inst. H. Poincarè, 46:4 (1987), 353–372 | MR | Zbl

[11] Harrel E. M., Commun. Math. Phys., 75 (1980), 239–261 | DOI | MR | Zbl

[12] Gutzuiller M. G., Chaos in classical and quantum mechanics, Springer, 1990 | MR

[13] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1971 | MR

[14] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Nauka, M., 1971 | MR