3D Schrödinger equation: scattering operator, scattering amplitude and ergodic property

Abstract

Stationary scattering problem (when the distance $r$ tends to infinity) and dynamical scattering problem (when the time $t$ tends to infinity) are considered for the 3D Schrödinger equation. A simple interconnection between the scattering amplitude (stationary case) and scattering operator (dynamical case) is given in the paper. This result is a quantum mechanical analog of the ergodic formulas in the classical mechanics.

This paper is a further development of our results in arXiv:1809.03998 and arXiv:1801.05370

References in corpus (2)

• Relativistic Lippmann - Schwinger equation
• Eigenfunction expansions and scattering theory associated with Dirac equation

Cited by in corpus (1)

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