[en] We regard a current flow through an open one-dimensional quantum system which is determined by a dissipative Schroedinger operator. The imaginary part of the corresponding form originates from Robin boundary conditions with certain complex valued coefficients imposed on Schroedinger's equation. This dissipative Schroedinger operator can be regarded as a pseudo-Hamiltonian of the corresponding open quantum system. The dilation of the dissipative operator provides a (self-adjoint) quasi-Hamiltonian of the system, more precisely, the Hamiltonian of the minimal closed system which contains the open one is used to define physical quantities such as density and current for the open quantum system. The carrier density turns out to be an expression in the generalized eigenstates of the dilation while the current density is related to the characteristic function of the dissipative operator. Finally a rigorous setup of a dissipative Schroedinger-Poisson system is outlined