Note on the Retarded van der Waals Potential within the Dipole Approximation
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 b...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210714 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Note on the Retarded van der Waals Potential within the Dipole Approximation. Tadahiro Miyao. SIGMA 16 (2020), 036, 34 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 the atoms R is sufficiently large. We employ 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.
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| ISSN: | 1815-0659 |