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Note on the Retarded van der Waals Potential within the Dipole Approximation
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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We examine the dipole approximated Pauli–Fierz Hamiltonians of the nonrelativistic QED. We assume that the Coulomb potential of the nuclei together with the Coulomb interaction between the electrons can be approximated by harmonic potentials. By an exact diagonalization method, we prove that the binding energy of the two hydrogen atoms behaves as $R^{-7}$, provided that the distance between atoms $R$ is sufficiently large. We employ the Feynman's representation of the quantized radiation fields which enables us to diagonalize Hamiltonians, rigorously. Our result supports the famous conjecture by Casimir and Polder.
Keywords: retarded van der Waals potential, non-relativistic QED, Pauli–Fierz Hamiltonian
Mots-clés : dipole approximation. 
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     author = {Tadahiro Miyao},
     title = {Note on the {Retarded} van der {Waals} {Potential} within the {Dipole} {Approximation}},
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     year = {2020},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a35/}
}
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Tadahiro Miyao. Note on the Retarded van der Waals Potential within the Dipole Approximation. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a35/

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