Semiclassical Asymptotics for a Difference Schr\"odinger Equation with Two Coalescent Turning Points
Matematičeskie zametki, Tome 109 (2021) no. 6, pp. 948-953.

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

Keywords: difference Schrödinger equation, semiclassical approximation, coalescent turning points.
@article{MZM_2021_109_6_a14,
     author = {A. A. Fedotov},
     title = {Semiclassical {Asymptotics} for a {Difference} {Schr\"odinger} {Equation} with {Two} {Coalescent} {Turning} {Points}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {948--953},
     publisher = {mathdoc},
     volume = {109},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a14/}
}
TY  - JOUR
AU  - A. A. Fedotov
TI  - Semiclassical Asymptotics for a Difference Schr\"odinger Equation with Two Coalescent Turning Points
JO  - Matematičeskie zametki
PY  - 2021
SP  - 948
EP  - 953
VL  - 109
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a14/
LA  - ru
ID  - MZM_2021_109_6_a14
ER  - 
%0 Journal Article
%A A. A. Fedotov
%T Semiclassical Asymptotics for a Difference Schr\"odinger Equation with Two Coalescent Turning Points
%J Matematičeskie zametki
%D 2021
%P 948-953
%V 109
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a14/
%G ru
%F MZM_2021_109_6_a14
A. A. Fedotov. Semiclassical Asymptotics for a Difference Schr\"odinger Equation with Two Coalescent Turning Points. Matematičeskie zametki, Tome 109 (2021) no. 6, pp. 948-953. http://geodesic.mathdoc.fr/item/MZM_2021_109_6_a14/

[1] M. V. Fedoryuk, Asimptoticheskie metody dlya lineinykh obyknovennykh differentsialnykh uravnenii, Nauka, M., 1983 | MR | Zbl

[2] Y. Shibuya, Global Theory of Second Order Linear Ordinary Differential Equations with a Polynomial Coefficient, Amsterdam, North-Holland, 1975 | MR

[3] W. Wasow, Asymptotic expansions for ordinary differential equations, Dover Publ., New York, 1987 | MR

[4] V. S. Buslaev, A. A. Fedotov, Algebra i analiz, 6:3 (1994), 59–83 | MR | Zbl

[5] A. A. Fedotov, E. V. Schetka, Matematicheskie voprosy teorii rasprostraneniya voln. 45, Zap. nauchn. sem. POMI, 438, POMI, SPb., 2015, 236–254 | MR

[6] A. A. Fedotov, E. V. Schetka, Algebra i analiz, 29:2 (2017), 193–219

[7] A. Fedotov, F. Klopp, SIAM J. Math. Anal., 51:6 (2019), 4413–4447 | DOI | MR

[8] A. A. Fedotov, F. Klopp, “WKB asymptotics of meromorphic solutions to difference equations”, Appl. Anal., 2019 | DOI

[9] F. W. J. Olver, Philos. Trans. Roy. Soc. London Ser. A, 278:1279 (1975), 137–174 | MR

[10] W. Wasow, Linear Turning Point Theory, Springer, New York, 1985 | MR

[11] S. Yu. Slavyanov, Asymptotic Solutions of the One-Dimentional Schrödinger Equation, Transl. Math. Monogr., 151, Amer. Math. Soc., Providence, RI, 1996 | MR

[12] A. Yu. Anikin, S. Yu. Dobrokhotov, A. V. Tsvetkova, “Funktsii Eiri i perekhod ot kvaziklassicheskogo k ostsillyatornomu priblizheniyu dlya odnomernykh svyazannykh sostoyanii”, TMF, 204:2 (2020), 171–180 | DOI | MR

[13] M. Wilkinson, J. Phys. A, 20:13 (1987), 4337-4354 | DOI | MR

[14] A. Avila, S. Jitomirskaya, Ann. of Math. (2), 170 (2009), 303–342 | DOI | MR

[15] B. Helffer, J. Sjöstrand, Mém. Soc. Math. France (N.S.), 39 (1989), 1–124 | MR

[16] A. A. Fedotov, Algebra i analiz, 25:2 (2013), 203–235 | MR | Zbl

[17] A. A. Fedotov, E. V. Schetka, Matem. zametki, 107:6 (2020), 948–953 | DOI | MR

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

[19] Spravochnik po spetsialnym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, eds. M. Abramovits, I. Stigan, Nauka, M., 1979 | MR | Zbl