Scattering by a reflectionless modified P\"oschl-Teller potential: Bohmian trajectories and arrival times

TL;DR

This paper investigates the behavior of nonreflecting wavepackets in a reflectionless P"oschl-Teller potential, analyzing Bohmian trajectories and arrival times to understand quantum scattering and tunneling effects.

Contribution

It introduces a method to construct nonreflecting wavepackets from reflectionless eigenstates and compares their dynamics and arrival times with free particles, providing new insights into quantum scattering.

Findings

Mean arrival time depends on particle mass.

Bohmian trajectories differ significantly in the presence of the potential.

Nonreflecting wavepackets exhibit unique propagation characteristics.

Abstract

A nonreflecting wavepacket is constructed by the superposition of reflectionless eigenstates of sech2 potential. Free propagation and propagation in the presence of the above potential of such a wavepacket is considered using the concept of arrival time. Comparison is made with the free evolving Gaussian wavepacket. Mean arrival time at a detector behind the well is given as a function of mass for separate cases. A selection of Bohmian trajectories in the interacting case are computed and compared to the trajectories of a free particle guided by a Gaussian packet.