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On the dipole approximation with error estimates

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Abstract

The dipole approximation is employed to describe interactions between atoms and radiation. It essentially consists of neglecting the spatial variation of the external field over the atom. Heuristically, this is justified by arguing that the wavelength is considerably larger than the atomic length scale, which holds under usual experimental conditions. We prove the dipole approximation in the limit of infinite wavelengths compared to the atomic length scale and estimate the rate of convergence. Our results include N-body Coulomb potentials and experimentally relevant electromagnetic fields such as plane waves and laser pulses.

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Acknowledgements

We thank Detlef Dürr and Peter Pickl for many helpful discussions and the referees for their advice.

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Authors and Affiliations

  1. Fachbereich Mathematik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany

    Lea Boßmann

  2. Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstr. 39, 80333, Munich, Germany

    Lea Boßmann & Robert Grummt

  3. Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098, Paderborn, Germany

    Martin Kolb

Authors
  1. Lea Boßmann
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  2. Robert Grummt
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  3. Martin Kolb
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Correspondence to Lea Boßmann.

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Boßmann, L., Grummt, R. & Kolb, M. On the dipole approximation with error estimates. Lett Math Phys 108, 185–193 (2018). https://doi.org/10.1007/s11005-017-0999-y

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  • DOI: https://doi.org/10.1007/s11005-017-0999-y

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