Geodesic
An analogue of the Feynman–Kac formula for the multidimensional Shrödinger equation
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 34, Tome 525 (2023), pp. 96-108 
M. V. Platonova. An analogue of the Feynman–Kac formula for the multidimensional Shrödinger equation. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 34, Tome 525 (2023), pp. 96-108. http://geodesic.mathdoc.fr/item/ZNSL_2023_525_a7/
@article{ZNSL_2023_525_a7,
     author = {M. V. Platonova},
     title = {An analogue of the {Feynman{\textendash}Kac} formula for the multidimensional {Shr\"odinger} equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {96--108},
     year = {2023},
     volume = {525},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_525_a7/}
}
TY  - JOUR
AU  - M. V. Platonova
TI  - An analogue of the Feynman–Kac formula for the multidimensional Shrödinger equation
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2023
SP  - 96
EP  - 108
VL  - 525
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2023_525_a7/
LA  - ru
ID  - ZNSL_2023_525_a7
ER  - 
%0 Journal Article
%A M. V. Platonova
%T An analogue of the Feynman–Kac formula for the multidimensional Shrödinger equation
%J Zapiski Nauchnykh Seminarov POMI
%D 2023
%P 96-108
%V 525
%U http://geodesic.mathdoc.fr/item/ZNSL_2023_525_a7/
%G ru
%F ZNSL_2023_525_a7

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A probabilistic approximation of the solution of the Cauchy problem for the multidimensional Schrödinger equation with limited potential is constructed. The approximation has the form of expectations of functionals of a random point field.

[1] Dzh. Glimm, A. Dzhaffe, Matematicheskie metody v kvantovoi fizike, Mir, M., 1984

[2] Yu. L. Daletskii, S. V. Fomin, Mery i differentsialnye uravneniya v funktsionalnykh prostranstvakh, Nauka, M., 1983

[3] N. Danford, Dzh. Shvarts, Lineinye operatory. Obschaya teoriya, Izdatelstvo inostrannoi literatury, M., 1962

[4] P. N. Ievlev, “Veroyatnostnoe predstavlenie resheniya zadachi Koshi dlya mnogomernogo uravneniya Shredingera”, Zap. nauchn. semin. POMI, 466, 2017, 145–158

[5] I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Ob odnoi predelnoi teoreme, svyazannoi s veroyatnostnym predstavleniem resheniya zadachi Koshi s operatorom Shredingera”, Zap. nauchn. semin. POMI, 454, 2016, 158–175

[6] I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Veroyatnostnaya approksimatsiya operatora evolyutsii”, Funkts. analiz i ego pril., 52:2 (2018), 25–39

[7] T. Kato, Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972

[8] Dzh. Kingman, Puassonovskie protsessy, MTsNMO, M., 2007

[9] M. V. Platonova, “O veroyatnostnoi approksimatsii odnoi gruppy unitarnykh operatorov”, Zap. nauchn. semin. POMI, 510, 2022, 211–224

[10] O. G. Smolyanov, E. T. Shavgulidze, Kontinualnye integraly, LENAND, M., 2015