Relativistic Lippmann - Schwinger equation
Lev Sakhnovich
TL;DR
This paper develops a relativistic version of the Lippmann-Schwinger equation for the Dirac equation, representing it in integral form and analyzing both stationary and dynamical scattering problems.
Contribution
It introduces a novel integral form of the relativistic Lippmann-Schwinger equation for the Dirac equation and applies it to scattering problems.
Findings
Derived the integral form of the relativistic Lippmann-Schwinger equation.
Analyzed stationary scattering problems in the relativistic context.
Investigated dynamical scattering problems using the new integral equation.
Abstract
The classical Lippmann-Schwinger equation plays an important role in the scattering theory (non-relativistic case, Schr\"odinger equation). In the present paper we consider the relativistic analogue of the Lippmann-Schwinger equation. We represent the corresponding equation in the integral form. Using this integral equation we investigate the stationary scattering problems (relativistic case, Dirac equation). We consider the dynamical scattering problems (relativistic case, Dirac equation) as well.
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Taxonomy
TopicsAtomic and Molecular Physics · Quantum Mechanics and Non-Hermitian Physics · Quantum chaos and dynamical systems