Geodesic
The semiclassical approximation in quantum mechanics. A new approach
Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 1, pp. 48-55 
V. G. Bagrov; V. V. Belov; M. F. Kondrat'eva. The semiclassical approximation in quantum mechanics. A new approach. Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 1, pp. 48-55. http://geodesic.mathdoc.fr/item/TMF_1994_98_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown, that the quasiclassical approximation in quantum mechanics is equivalent to substitution of Schrödinger equation for finite closed system of ordinary differential equations of the first order with initial conditions, which satisfy special restrictions.

[1] Grin Kh., Matrichnaya kvantovaya mekhanika, Mir, M., 1968 | MR

[2] Maslov V. P., Teoriya vozmuschenii i asimptoticheskie metody, Izd-vo MGU, M., 1965 | MR

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

[4] Maslov V. P., Asimptoticheskie metody i teoriya vozmuschenii, Nauka, M., 1988 | MR

[5] Buslaev V. S., Funkts. analiz i ego prilozh., 3:3 (1969), 17–31 | MR | Zbl

[6] Kucherenko V. V., Izv. AN SSSR. Ser. matem., 38 (1974), 625–662 | MR | Zbl

[7] Lere Zh., Lagranzhev analiz i kvantovaya mekhanika, Mir, M., 1981 | MR

[8] Dobrokhotov S. Yu., Maslov V. P., Sovr. probl. matem., 17, VINITI, 1980, 3–91 | MR

[9] Danilov V. G., Maslov V. P., Sovr. probl. matem., 6, VINITI, 1975, 5–132 | MR

[10] Mischenko A. S., Sternin B. Yu., Shatalov V. E., Lagranzhevy mnogoobraziya i metod kanonicheskogo operatora, Nauka, M., 1978 | MR

[11] Belov V. V., Dobrokhotov S. Yu., DAN SSSR, 298:5 (1988), 1037–1042 | MR | Zbl

[12] Belov V. V., Dobrokhotov S. Yu., Kvaziklassicheskie asimptotiki Maslova v spektralnykh kvantovykh zadachakh, sootvetstvuyuschikh chastichno integriruemym gamiltonovym sistemam, Preprint, MIAN, M., 1988 | MR

[13] Karasev M. V., Maslov V. P., Izv. AN SSSR. Ser. matem., 47:5 (1983), 999–1029 | MR | Zbl

[14] Dodonov V. V., Manko V. P., Trudy FIAN, 183, 5–70 | MR

[15] Bagrov V. G., Belov V. V., Ternov I. M., TMF, 50:3 (1982), 390–396 | MR

[16] Bagrov V. G., Belov V. V., Ternov I. M., J. Math. Phys., 24:12 (1983), 2855–2859 | DOI | MR

[17] Rogova A. M., Dep. v VINITI, No 129–B9, VINITI, M., 1992

[18] Belov V. V., Maslov V. P., DAN SSSR, 311:4 (1990), 849–854 | MR

[19] Belov V. V., Kondrateva M. F., TMF, 92:1 (1992), 41–60 | MR

[20] Wong S. K., Nuovo Cim., LXV A:4 (1970), 689–694 | DOI