We give error bounds of the Trotter-Kato product formula of
relativistic Schrödinger operators
$\sqrt{(i \partial_x - a(x))^2 + 1} - 1 + V(x)$,
where $B(x) = \nabla \times a(x)$
is bounded and $V(x)$ behaves like $|x|^{\rho}$,
$\rho > 0$.
@article{1148393579,
author = {Doumeki, Atsushi},
title = {Error bounds on the Trotter-Kato product formula of relativistic Schr\"odinger operators with electromagnetic fields},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {76},
number = {10},
year = {2000},
pages = { 7-12},
language = {en},
url = {http://dml.mathdoc.fr/item/1148393579}
}
Doumeki, Atsushi. Error bounds on the Trotter-Kato product formula of relativistic Schrödinger operators with electromagnetic fields. Proc. Japan Acad. Ser. A Math. Sci., Tome 76 (2000) no. 10, pp. 7-12. http://gdmltest.u-ga.fr/item/1148393579/