Related papers: Note on the Retarded van der Waals Potential withi…
The analysis of correlation energy of the simplest first approximation of a variational method for the intrashell states of two-electron atoms is the purpose of the present work. This method allows to divide energy of atom on Coulomb and…
We consider the semi-relativistic Pauli-Fierz Hamiltonian and a no-pair model of a hydrogen-like atom interacting with a quantized photon field at the respective critical values of the Coulomb coupling constant. For arbitrary values of the…
Taking into account results of WKB-approximation, we derive exact quantum energies and wave functions of even and odd states in the one-dimensional Coulomb potential
We derive the ground state energy up to the fourth order in the fine structure constant $\alpha$ for the translation invariant Pauli-Fierz Hamiltonian for a spinless electron coupled to the quantized radiation field. As a consequence, we…
A calculation of the QED vacuum polarization potential in the Coulomb field of a pointlike nucleus was presented in an earlier publication by the author and his collaborators. Corrections up to order $\alpha^2 (Z\alpha)^7$ were evaluated,…
In calculating the energy corrections to the hydrogen levels we can identify two different types of modifications of the Coulomb potential $V_{C}$, with one of them being the standard quantum electrodynamics corrections, $\delta V$,…
Based on classical electrodynamics, it is argued that the Coulomb potential (which is strictly valid for two point charges at rest), commonly used in the study of energy levels of hydrogen atom is not the correct one, because the electron…
We consider atoms or molecules coupled to the quantized electromagnetic radiation field in a dipole approximation. We show the existence of ground states and resonance states in situations where the eigenvalues are degenerate and protected…
We calculate pair potential curves for interacting Rydberg atoms in a constant electric field and use them to determine the effective $C_3$ dipole-dipole and $C_6$ van der Waals coefficients. We compare the $C_3$ and $C_6$ with experiments…
We consider the van der Waals energy of an atom near the infinitely thin sphere with finite conductivity which model the fullerene. We put the sphere into spherical cavity inside the infinite dielectric media, then calculate the energy of…
We consider a hydrogen-like atom in a quantized electromagnetic field which is modeled by means of the semi-relativistic Pauli-Fierz operator and prove that the infimum of the spectrum of the latter operator is an eigenvalue. In particular,…
The structure and stability of atomic and molecular systems with van der Waals (vdW) bonding are often determined by the interplay between attractive dispersion interactions and repulsive interactions caused by electron confinement. Arising…
We compute the expectations of the squares of the electric and magnetic fields in the vacuum region outside a half-space filled with a uniform non-dispersive dielectric. This gives predictions for the Casimir-Polder force on an atom in the…
We study the energy of relativistic electrons and positrons interacting via the second quantized Coulomb potential in the field of a nucleus of charge Z within the Hartree-Fock approximation. We show that the associated functional has a…
A simple and computationally efficient scheme to calculate approximate imaginary-frequency dependent polarizability, hence asymptotic van der Waals coefficient, within density functional theory is proposed. The dynamical dipolar…
We review our recent progress in the determination of the high-density correlation energy $\Ec$ in two-electron systems. Several two-electron systems are considered, such as the well known helium-like ions (helium), and the Hooke's law atom…
We provide a theoretical description for the coupling between the intersubband excitations of a bi-dimensional electron gas with the electromagnetic field. This description, based on the electrical dipole gauge, applies to an arbitrary…
We analyze the supersymmetric features of isolated double-well potentials, both symmetric ones and ones under an asymmetric perturbation. Our studies are in concert with results obtained elsewhere. Further on, a particular interest is paid…
In this work we investigate the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian. We use our recently developed method based on…
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…