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  • Open Access

Helical quantum two-body problem and its wave packet dynamics

Peter Schmelcher*

  • Zentrum für Optische Quantentechnologien, Fachbereich Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany

  • *Contact author: peter.schmelcher@uni-hamburg.de
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APS Open Sci. 1, 000032 – Published 29 May, 2026

DOI: https://doi.org/10.1103/hh2r-zqdl

Abstract

We explore the helical quantum two-body problem, i.e., two repulsively Coulomb interacting particles confined to move along a helix. The effective potential possesses a tunable number of potential wells superimposed on the repulsive Coulomb interaction that can be varied by changing the ratio of the pitch and radius of the helix. The anharmonicity of these wells depends crucially on this ratio and on the order of the well, which can also be seen by analyzing the individual wells’ energy eigenvalue spacing. Our main focus is the investigation of the quantum dynamics of differently prepared wave packets that scatter from the multiwell potential landscape. We show that there exists a rich pattern-forming transient evolution that depends also on the number of bound states of the individual wells. We demonstrate how the multiple wells leave their fingerprints in the dynamics leading, among others, to oscillatory structures on different spatial scales, the formation of beats, and pulsed emission from single well localized wave packets due to their intrawell dynamics.

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APS Open Sci. 1, 000032– Published 29 May, 2026
Vol. 1
  • Received 10 March 2026
  • Accepted 18 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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