NON-MARKOVIAN OPEN-SYSTEM BOUNDARY-CONDITIONS FOR THE TIME-DEPENDENT SCHRODINGER-EQUATION

The open-system boundary conditions for the one-dimensional Schrodinge r equation are derived by dividing the unbounded domain into a finite system and two semi-infinite reservoirs. The resulting boundary condit ions on the system are non-Markovian, as they contain a convolution ov er the history of the system. Thus, time-irreversibility arises in a p ure-state problem, The propagator which appears in the boundary condit ion is derived for a simple discrete model. The correctness of the bou ndary conditions is verified and the usefulness of the discrete model is demonstrated by a numerical calculation of the time-evolution of a wave packet.