Geodesic
Asymptotic behavior of solutions to a nonstationary equation Schrödinger on a semi-axle with a potential which is slowly depends on time
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 51, Tome 506 (2021), pp. 245-257 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The asymptotic behavior of the solutions of the Cauchy problem for the nonstationary Schrödinger equation on the semiaxis with a rapidly decreasing potential is studied. The construction of asymptotic solutions is based on the spectral expansion of the solution at a given time. This construction does not use the adiabatic theorem of scattering theory. In the highest order (as in the approach associated with the adiabatic theorem of scattering theory), the solution does not depend on the dynamics of the potential and is completely determined by the value of the potential at the zero instant of time. In this paper, we calculated power-law corrections to the leading term of the solution associated with the boundary of the continuous spectrum, which take into account the time dependence of the operator. 
@article{ZNSL_2021_506_a15,
     author = {V. V. Sukhanov},
     title = {Asymptotic behavior of solutions to a nonstationary equation {Schr\"odinger} on a semi-axle with a potential which is slowly depends on time},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {245--257},
     year = {2021},
     volume = {506},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a15/}
}
TY  - JOUR
AU  - V. V. Sukhanov
TI  - Asymptotic behavior of solutions to a nonstationary equation Schrödinger on a semi-axle with a potential which is slowly depends on time
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2021
SP  - 245
EP  - 257
VL  - 506
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a15/
LA  - ru
ID  - ZNSL_2021_506_a15
ER  - 
%0 Journal Article
%A V. V. Sukhanov
%T Asymptotic behavior of solutions to a nonstationary equation Schrödinger on a semi-axle with a potential which is slowly depends on time
%J Zapiski Nauchnykh Seminarov POMI
%D 2021
%P 245-257
%V 506
%U http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a15/
%G ru
%F ZNSL_2021_506_a15
V. V. Sukhanov. Asymptotic behavior of solutions to a nonstationary equation Schrödinger on a semi-axle with a potential which is slowly depends on time. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 51, Tome 506 (2021), pp. 245-257. http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a15/

[1] J. D. Dollard, “Adiabatic switching in the Shroedinger theory of scattering”, J. Math. Phys., 7 (1966), 802–810 | DOI | MR

[2] G. Nenciu, “On the adiabatic limit for Dirac particles in external fields”, Com. Math. Phys., 76 (1980), 117–128 | DOI | Zbl

[3] A. Martinez, Sh. Nakamura, “Adiabatic limit and scattering”, C. R. Acad. Sci. Paris ser I Math., 318:12 (1994), 1153–1158 | MR | Zbl

[4] V. V. Sukhanov, “Asimptoticheskoe povedenie reshenii nestatsionarnogo uravneniya Diraka s medlenno zavisyaschim ot vremeni potentsialom”, Zap. nauchn. semin. POMI, 483, 2019, 189–198

[5] V. V. Sukhanov, “Asimptoticheskoe povedenie reshenii nestatsionarnogo uravneniya Shredingera s medlenno zavisyaschim ot vremeni potentsialom”, Zap. nauchn. semin. POMI, 493, 2020, 323–335

[6] V. A. Marchenko, Sturm-Liouville operators and their applications, “Naukova Dumka”, Kiev, 1977 (Russian) | Zbl