Quantum reflection time and the Goos-H\"anchen effect

TL;DR

This paper investigates quantum reflection delays and the Goos-H"anchen effect, showing how potential representations affect measured times and calculating lateral shifts for Gaussian beams at potential interfaces.

Contribution

It introduces a method to replace soft potentials with superpositions of hard walls for analyzing quantum reflection and the Goos-H"anchen shift.

Findings

Negative quantum reflection times can occur and are best avoided.

Superpositions of hard walls can effectively model soft potentials.

Calculated Goos-H"anchen shifts for Gaussian beams at potential steps and barriers.

Abstract

We explore the analogy between following the motion of a reflected wave packet, and a quantum measurement of the spatial delay imposed on the particle by the scattering potential. It is shown that converting such delays into temporal durations can lead to "negative times", and best be avoided. It is also demonstrated that a "soft" potential can be replaced by superposition of hard walls. This representation is used for calculating the Goos-H\"anchen shift of a Gaussian beam incident on a potential step or a barrier at an oblique angle.