Scattering from a discrete quasi-Hermitian delta function potential

Amine B Hammou

Scattering from a discrete quasi-Hermitian delta function potential is studied and the metric operator is found. A generalized continuity relation in the physical Hilbert space $${\mathcal H}_{{\rm phys}}$$ is derived and the probability current density is defined. The reflection $${\mathcal R}$$ and transmission $${\mathcal T}$$ coefficients computed with this current are shown to obey the unitarity relation $${\mathcal R}+{\mathcal T}=1$$.

http://dx.doi.org/10.1088/1751-8113/45/21/215310