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We investigate wavepacket solutions for time-dependent Schoedinger equationin the presence of an exponentially decaying potential. Assuming for travellingwave solutions the phase to be a linear combination of the space and timecoordinates, we obtain two distinct wavepacket solutions for the Schroedingerequation. The wavepackets counterpropagate in space at a constant velocitywithout any distortion or spreading thus retain their initial form atarbitrarily large distances.

Counterpropagating Wavepacket Solutions of the Time-Dependent Schroedinger Equation for a Decaying Potential Field