Dirac equation: the stationary and dynamical scattering problems (Q1626079)

The paper considers the radial Dirac system \[ \begin{aligned} \left(\frac{\mathrm{d}}{\mathrm{d}r}+\frac{k}{r}\right)f-(\lambda+m-v(r))g = 0\,,\\ \left(\frac{\mathrm{d}}{\mathrm{d}r}-\frac{k}{r}\right)g+(\lambda-m-v(r))f = 0 \end{aligned} \] with Coulomb-type potential \[ v(r) = -\frac{A}{r}+q(r) \] with \(A, k, q(r) \in \mathbb{R}\), \(m>0\), \(|k|>|A|\) and \(q\) satisfying \[ \int_0^\infty (1+r)|q(r)|\,\mathrm{d}r <\infty\,. \] For this system, the author proves that the action of the generalized dynamic scattering operator \(S_{\mathrm{dyn}}\) and of the generalized stationary scattering operator \(S_{\mathrm{st}}\) in a certain subspace of functions is the same. The claim is proven for both \(A\neq 0\) and \(A =0\). See also [the author, Complex Anal. Oper. Theory 12 (3), 767--776 (2018; Zbl 1390.34238)] and [the author, Complex Anal. Oper. Theory 12 (3), 607--613 (2018; Zbl 1390.34237)] for more details on this ergodicity-type theorem. For the entire collection see [Zbl 1388.46001].