Geodesic
Quasiclassical asymptotic behaviors for discrete models of electron-phonon interaction: Maslov's method and the adiabatic approximation
Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 1, pp. 63-74 
Yu. M. Vorob'ev; S. Yu. Dobrokhotov. Quasiclassical asymptotic behaviors for discrete models of electron-phonon interaction: Maslov's method and the adiabatic approximation. Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 1, pp. 63-74. http://geodesic.mathdoc.fr/item/TMF_1983_57_1_a7/
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     title = {Quasiclassical asymptotic behaviors for discrete models of electron-phonon interaction: {Maslov's} method and the adiabatic approximation},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The eigenvalue problem for a quantum model of electron-phonon interaction on a discrete Iattice is treated as an equation with operator coefficients, and Maslov's operator method is used to construct series of asymptotic eigenfunctions and eigenvalues with respect to the small parameter corresponding to the interaction of the light and heavy particles.

[1] Su W. P., Schrieffer I. R., Heeger A. I., Phys. Rev., B22:4 (1980), 2099–2112

[2] Paierls R., Kvantovaya teoriya tverdykh tel, IL, M., 1956

[3] Brazovskii S. A., Dzyaloshinskii I. E., Krichever I. M., ZhETF, 83:7 (1982), 389–415 | MR

[4] Maslov V. P., Teoriya vozmuschenii i asimptoticheskie metody, MGU, M., 1965 | MR

[5] Maslov V. P., “Metod VKB v mnogomernom sluchae”, Prilozhenie k kn.: Dzh. Kheding, Vvedenie v metod fazovykh integralov, Mir, M., 1965

[6] Maslov V. P., Operatornye metody, Nauka, M., 1973 | MR

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

[8] Maslov V. P., Fedoryuk M. V., Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, Nauka, M., 1976 | MR

[9] Karasev M. V., Zadachnik po operatornym metodam, MIEM, M., 1979

[10] Zaiman Dzh., Printsipy teorii tverdogo tela, Mir, M., 1974

[11] Kucherenko V. V., Izv. AN SSSR, ser. matem., 38:3 (1974), 625–662 | Zbl

[12] Karasev M. V., Maslov V. P., Itogi nauki i tekhn. Sovrem. probl. mat., 13, VINITI, M., 1979, 145–266 | MR

[13] Krakhnov A. D., UMN, 31:3 (1976), 217–218 | MR | Zbl

[14] Kirillov A. A., Elementy teorii predstavleniya, Nauka, M., 1972 | MR

[15] Krichever I. M., UMN, 33:4 (1978), 215–216 | MR | Zbl

[16] Dobrokhotov S. Yu., Maslov V. P., Itogi nauki i tekhn. Sovrem. probl. mat., 15, VINITI, M., 1980, 3–94

[17] Dubrovin B. A., Matveev V. B., Novikov S. Ya., UMN, 31:1 (1976), 55–136 | MR | Zbl

[18] Ferguson W. E., Flaschka H., McLaughlin D. W., J. Comput. Phys., 45:2 (1982), 157–209 | DOI | MR | Zbl