%0 Journal Article
%T Non-Hermitian quantum mechanics: the case of bound state scattering theory
%A A. Matzkin
%J Mathematics
%D 2006
%I arXiv
%R 10.1088/0305-4470/39/34/017
%X Excited bound states are often understood within scattering based theories as resulting from the collision of a particle on a target via a short-range potential. We show that the resulting formalism is non-Hermitian and describe the Hilbert spaces and metric operator relevant to a correct formulation of such theories. The structure and tools employed are the same that have been introduced in current works dealing with PT-symmetric and quasi-Hermitian problems. The relevance of the non-Hermitian formulation to practical computations is assessed by introducing a non-Hermiticity index. We give a numerical example involving scattering by a short-range potential in a Coulomb field for which it is seen that even for a small but non-negligible non-Hermiticity index the non-Hermitian character of the problem must be taken into account. The computation of physical quantities in the relevant Hilbert spaces is also discussed.
%U http://arxiv.org/abs/quant-ph/0603238v1