Geodesic
Asymptotic solutions of the Schrödinger equation in thin tubes
Trudy Instituta matematiki i mehaniki, Asymptotic expansions, approximation theory, topology, Tome 9 (2003) no. 1, pp. 15-25 Cet article a éte moissonné depuis la source Math-Net.Ru

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V. V. Belov; S. Yu. Dobrokhotov; S. O. Sinitsyn. Asymptotic solutions of the Schrödinger equation in thin tubes. Trudy Instituta matematiki i mehaniki, Asymptotic expansions, approximation theory, topology, Tome 9 (2003) no. 1, pp. 15-25. http://geodesic.mathdoc.fr/item/TIMM_2003_9_1_a2/

[1] Babich V. M., Buldyrev B. C., Molotkov I. A., Prostranstvenno-vremennoi luchevoi metod, L., 1985, 120 pp.

[2] Baz A. M., Zeldovich Ya. B., Perelomov A. M., Rasseyanie, reaktsii i raspady v nerelyativistskoi mekhanike, Nauka, M., 1971, 370 pp. | Zbl

[3] Belov V. V., “Kvaziklassicheskie urovni energii dvukhatomnoi molekuly v magnitnom pole”, Izv. vuzov. Matematika, 1976, no. 6, 13–18

[4] Belov V. V., Baranov V. A., “Kvaziklassicheskie kvazienergeticheskie sostoyaniya dlya odnomernogo uravneniya Shredingera”, Izv. vuzov. Fizika, 1999, no. 10, 30–36

[5] Belov V. V., Maslov V. P., “Kvaziklassicheskie traektorno-kogerentnye sostoyaniya v kvantovoi mekhanike s kalibrovochnymi polyami”, Dokl. AN SSSR, 311:4 (1990), 849–854 | MR

[6] Belov V. V., Maslov V. P., “Kvaziklassicheskie traektorno-kogerentnye sostoyaniya dlya uravneniya Diraka s anomalnym vzaimodeistviem Pauli”, Dokl. AN SSSR, 305:3 (1989), 764–780

[7] Belov V. V., Rogova A. M., Trifonov A. Yu., “Kvazienergeticheskie sostoyaniya i ravnomernye po vremeni asimptotiki”, Izv. vuzov. Fizika, 1999, no. 7, 24–30. | MR

[8] Berezin F. A., Shubin M. A., Uravnenie Shredingera, Izd-vo MGU, M., 1983, 392 pp. | MR

[9] Buslaev B. C., “Kvaziklassicheskoe priblizhenie dlya uravnenii s periodicheskimi koeffitsientami”, Uspekhi mat. nauk, 42:6(258) (1987), 77–98 | MR | Zbl

[10] Buslaev B. C., “Adiabaticheskoe vozmuschenie periodicheskogo potentsiala”, Teoret. i mat. fizika, 58:2 (1984), 233–243 | MR | Zbl

[11] Vorobev E. M., Maslov V. P., “Ob odnomodovykh otkrytykh rezonatorakh”, Dokl. AN SSSR, 179:10 (1968), 558–561

[12] Dobrokhotov S. Yu., “Prilozhenie teorii Maslova k dvum uravneniyam s operatornoznachnym simvolom”, Uspekhi mat. nauk, 39:4(238) (1984), 125 | MR

[13] Dobrokhotov S. Yu., “Rezonansy v asimptotike resheniya zadachi Koshi dlya uravneniya Shredingera s bystroostsilliruyuschim konechnozonnym potentsialom”, Mat. zametki, 44:3 (1988), 319–340 | MR | Zbl

[14] Zeldovich Ya. B., “Kvazienergiya kvantovoi sistemy, podvergayuschayasya periodicheskomu vozdeistviyu”, Zhurn. eksperiment. i teoret. fiziki, 51:5 (1966), 1492–1495

[15] T. Tamir (red.), Integralnaya optika, Mir, M., 1978, 344 pp.

[16] Korn G., Korn T., Spravochnik po matematike, Nauka, M., 1968, 720 pp. | MR

[17] Landau L. D., Lifshits E. M., Kvantovaya mekhanika, Nauka, M., 1998 | MR

[18] Lifshits E. M., Pitaevskii L. P., Statisticheskaya fizika, Chast 2, Nauka, M., 1978, 448 pp. | MR

[19] Maslov V. P., Teoriya vozmuschenii i asimptoticheskie metody, MGU, M., 1965, 549 pp.

[20] Maslov V. P., Fedoryuk M. V., Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, Nauka, M., 1976, 296 pp. | MR

[21] Polyanin A. D., Spravochnik po lineinym uravneniyam matematicheskoi fiziki, Fiz.-mat. lit., M., 2001, 576 pp.

[22] Berry M. V., “Quantum phase factors accompanying adiabatic changes”, Proc. Roy. Soc. London A, 392:1802 (1984), 45–48 | DOI | MR

[23] Bruning J., Dobrokhotov S. Yu., Pankrashkin K. V., “The spectral asymptotics of the strong magnetic field. I”, Russ. J. Math. Phys., 9:1 (2002), 14–49 | MR

[24] Duclos P., Exner P., “Curvature-induced bound states in quantum waveguides in two and three dimensions”, Rev. Math. Phys., 7 (1995), 73–102 | DOI | MR | Zbl

[25] Duclos P., Exner P., Krejčiřík D., “Bound states in curved quantum layers”, Commun. Math. Phys., 223 (2001), 13–28 | DOI | MR | Zbl

[26] Duclos P., Exner P., Krejčiřík D., “Locally curved quantum layers”, Ukrainian J. Phys., 45 (2000), 595–601 | MR

[27] Exner P., “A quantum pipette”, J. Math. Phys. A, 28 (1995), 5323–5330 | DOI | MR | Zbl

[28] Entin M. V., Magarill L. I., “Electrons in a twisted quantum wire”, Phys. Rev. B, 66 (2002), 205308 | DOI

[29] Helffer B., Semi-classical analysis for the Schrodinger operator and applications, Lect. Notes Math., 1336, 1988, 107 pp. | MR | Zbl

[30] Maslov V. P., Mathematical aspects of integral optics, MIEM, M., 1983, 130 pp.

[31] Maslov V. P., “Mathematical aspects of integral optics”, Russ. J. Math. Phys., 8:2 (2001), 180–238 | MR | Zbl

[32] Prinz V. Ya., Golod S. V., Mashanov V. I., Gutakovsky A.K̇., Inst. Phys. Conf. Ser., 166 (2000), 203–206

[33] Prinz V. Ya., Grutzmacher D., Beyer A., David C., Ketterer B., Deckardt E., Nanotechnology, 2001, no. 12, 399–402 | DOI