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

Abstract

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.

This work is a continuation and essential further development of the results obtained in arXiv:1801.05370, arXiv:1809.03998, arXiv:1905.07608

References in corpus (2)

• Eigenfunction expansions and scattering theory associated with Dirac equation
• 3D Schrödinger equation: scattering operator, scattering amplitude and ergodic property