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Quantum reflection time and the Goos-Hänchen effect

Dmitri Sokolovski1,2,3,*, Anton Uranga1,3,4, and Yves Caudano5

  • 1Departamento de Química-Física, Universidad del País Vasco, UPV/EHU, 48940 Leioa, Spain
  • 2IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain
  • 3EHU Quantum Center, Universidad del País Vasco, UPV/EHU, 48940 Leioa, Spain
  • 4Basque Center for Applied Mathematics (BCAM), 48009 Bilbao, Spain
  • 5Department of Physics, Namur Institute for Complex Systems (naXys) and Namur Institute of Structured Matter (NISM), University of Namur, Rue de Bruxelles 61, 5000 Namur, Belgium

  • *Contact author: dgsokol15@gmail.com
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Phys. Rev. Research 8, 013084 – Published 26 January, 2026

DOI: https://doi.org/10.1103/4vcv-9z6q

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 a superposition of hard walls. This representation is used for calculating the Goos-Hänchen shift of a Gaussian beam incident on a potential step or a barrier at an oblique angle.

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Corrections

12 February, 2026

Correction: Figure 1 was incorrectly formatted and has been replaced.

Article Text

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Phys. Rev. Research 8, 013084– Published 26 January, 2026
  • Received 3 October 2025
  • Accepted 12 December 2025
  • Corrected 12 February 2026
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