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

TL;DR

This paper presents new counterpropagating wavepacket solutions to the time-dependent Schrödinger equation with an exponentially decaying potential, demonstrating non-spreading, distortion-free propagation at constant velocity.

Contribution

It introduces two novel wavepacket solutions that maintain their shape during propagation in a decaying potential, expanding understanding of quantum wave dynamics.

Findings

Wavepackets do not spread or distort over large distances.

Solutions are valid for exponentially decaying potentials.

Wavepackets propagate at constant velocity without dispersion.

Abstract

We investigate wavepacket solutions for time-dependent Schoedinger equation in the presence of an exponentially decaying potential. Assuming for travelling wave solutions the phase to be a linear combination of the space and time coordinates, we obtain two distinct wavepacket solutions for the Schroedinger equation. The wavepackets counterpropagate in space at a constant velocity without any distortion or spreading thus retain their initial form at arbitrarily large distances.