Schrodinger equation with imaginary potential

We numerically investigate the solution of the Schrodinger equation in a one-dimensional system with gain. The gain is introduced by adding a positive imaginary potential in the system. We find that the time-independent solution gives that the amplification suppresses wave transmission at large gain. Solutions from the time-dependent equation clearly demonstrate that when gain is above a threshold value, the amplitude of the transmitted wave increases exponentially with time. (C) 2001 Elsevier Science B.V. All rights reserved.