Lippmann-Schwinger equation and the connection between the scattering operator and the scattering amplitude in the relativistic case

Autor:	Sakhnovich, Lev
Rok vydání:	2019
Předmět:	Mathematical Physics Mathematics - Analysis of PDEs Mathematics - Dynamical Systems Mathematics - Spectral Theory 81T15 34L25 81Q05 81Q30
Druh dokumentu:	Working Paper
Popis:	In this paper, we consider two types of the scattering problems (relativistic case), namely, the stationary scattering problem, where the distance $r$ tends to infinity, and the dynamical scattering problem, where the time $t$ tends to infinity. Using our results on Lippmann-Schwinger equation in the relativistic case, we found the connection between the stationary scattering problem (the scattering amplitude) and the dynamical scattering problem (the scattering operator). This result is the quantum mechanical analog of the ergodic formulas in the classical mechanics. Comment: This work is a continuation and essential further development of the results obtained in arXiv:1801.05370, arXiv:1809.03998, arXiv:1905.07608
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1910.03682 Zobrazit plný text záznamu View this record from Arxiv