Note on the Retarded van der Waals Potential within the Dipole Approximation

Abstract

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.

References in corpus (1)

• Differentiability of the van der Waals interaction between two atoms

Cited by in corpus (1)

• Thermal stability of the Nagaoka-Thouless theorems