Related papers: Note on the Retarded van der Waals Potential withi…
In this review we consider two different models of a hydrogenic atom in a quantized electromagnetic field that treat the electron relativistically. The first one is a no-pair model in the free picture, the second one is given by the…
The retarded van-der-Waals potential, as first obtained by Casimir and Polder, is usually computed on the basis of nonrelativistic QED. The hamiltonian describes two infinitely heavy nuclei, charge $e$, separated by a distance $R$ and two…
Van der Waals interactions between two neutral but polarizable systems at a separation $R$ much larger than the typical size of the systems are at the core of a broad sweep of contemporary problems in settings ranging from atomic, molecular…
We consider two three-dimensional isotropic harmonic oscillators interacting with the quantum electromagnetic field in the Coulomb gauge and within dipole approximation. Using a Bogoliubov-like transformation, we can obtain transformed…
The atomic dipole polarizability, $\alpha$, and the van der Waals (vdW) radius, $R_{\rm vdW}$, are two key quantities to describe vdW interactions between atoms in molecules and materials. Until now, they have been determined independently…
We compute the interaction energies of a two-atom system placed in the middle of a perfectly reflecting planar cavity, in the perturbative regime. Explicit expressions are provided for the van der Waals potentials of two polarisable atomic…
In this work we present a set of virial relations for many electron systems coupled to field modes, described by the Pauli--Fierz Hamiltonian in dipole approximation and using length gauge. Currently, there is growing interest in solutions…
The Fourier component of the potential energy of interaction of an atom with an atom is represented as a polynomial of the fourth degree from the atomic form factor. A numerical calculation was performed for the atomic form factor in the…
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…
We study a system composed of a hydrogen atom interacting with an infinite conductor wall. The interaction energy decays like $L^{-3}$, where $L$ is the distance between the atom and the wall, due to the emergence of the van der Waals…
We show that the dipole-dipole interaction between two Rydberg atoms can give rise to long range molecules. The binding potential arises from two states that converge to different separated atom asymptotes. These states interact weakly at…
We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen in relativistic quantum mechanics. From mathematical viewpoint, the goal is equivalent to determination of the…
The non-relativistic static and dynamic dipole polarizabilities of hydrogen atom experiencing a cylindrical confinement are investigated. Two methods based on B-Splines are used for the computations of the energies and wavefunctions. The…
We consider a multiatomic system where the nuclei are assumed to be point charges at fixed positions. Particles interact via Coulomb potential and electrons have pseudo-relativistic kinetic energy. We prove the van der Waals-London law,…
We discuss the equivalent form of Levy-Leblond equation [1, 2] such that the nilpotent matrices are two dimensional. We show that this equation can be obtained in the non-relativistic limit of the (2+1) dimensional Dirac equation.…
We extend the class of QM problems which permit for quasi-exact solutions. Specifically, we consider planar motion of two interacting charges in a constant uniform magnetic field. While Turbiner and Escobar-Ruiz (2013) addressed the case of…
The van der Waals potential of two atoms in the presence of an arbitrary arrangement of dispersing and absorbing magnetodielectric bodies is studied. Starting from a polarizable atom placed within a given geometry, its interaction with a…
The problem of two electrons in a two-dimensional random potential is addressed numerically. Specifically, the role of the Coulomb interaction between electrons on localization is investigated by writing the Hamiltonian on a localized basis…
We show that two photons coupled to Rydberg states via electromagnetically induced transparency can interact via an effective Coulomb potential. This interaction gives rise to a continuum of two-body bound states. Within the continuum,…
The interaction of an electron with a local static charge distribution (e.g., an atom or molecule) is dominated at large distances by the radial 1/r Coulomb potential. The second order effect comes from the non-central electric dipole…