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Exact analytic expression is derived for the matrix elements of the Coulomb interaction in two dimensions in the form of a closed finite sum expression. The orthonormal complete set of eigenfunctions of the harmonic oscillator is used as…
We study the Casimir interaction between perfectly conducting sphere and plate in the classical limit of high temperatures. By taking the small-distance expansion of the exact scattering formula, we compute the leading correction to the…
In this paper we take up the quantal two-centre problem where the Coulomb centres have arbitrary positive charges. In analogy with the symmetric case, treated in the second paper of this series of papers, we use the knowledge on the…
An eikonal expansion is developed in order to provide systematic corrections to the eikonal approximation through order 1/k^2, where k is the wave number. The expansion is applied to wave functions for the Klein-Gordon equation and for the…
Within the framework of potential scattering theory we derive an analytical two-potential formula for the on-shell partial wave scattering amplitude. This formula embodies a large number of possible applications, including long range…
A very simple method is devised to derive a (strictly) isospectral extension of the Morse potential. Furthermore, point canonical transformations are used to transform the latter into quasi-exactly solvable extensions of the radial…
We present a unified framework for studying Coulomb interactions in arbitrary environments using macroscopic quantum electrodynamics on the basis of the electromagnetic Green's function. Our theory can be used to derive the Coulomb…
We present a simple method to deal with caustics in the semiclassical approximation to the partition function of a one-dimensional quantum system. The procedure, which makes use of complex trajectories, is applied to the quartic double-well…
We compute the Casimir interaction energy between two perfectly conducting, concentric cylinders, using the mode-by-mode summation technique. Then we compare it with the approximate results obtained using the proximity theorem and a…
Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize, thereby reducing the magnitude of the interaction. Exchange integrals of…
The Coulomb-gauge vector potential of a uniformly moving point charge is obtained by calculating the gauge function for the transformation between the Lorenz and Coulomb gauges. The expression obtained for the difference between the vector…
A theory describing above-threshold ionization of atoms and ions in a strong electromagnetic field is presented. It is based on the widely known strong field approximation and incorporates the Coulomb interaction between the photoelectron…
The oscillator representation method is presented and used to calculate the energy spectra for a superposition of Coulomb and power-law potentials and for Coulomb and Yukawa potentials. The method provides an efficient way to obtain…
We determine the interaction potential of a solitonic dipole in the singlet state, modeled as an SU(2) field, using improved lattice simulations of two stationary solitons at varying separations. The potential is extracted from the energy…
For the Casimir interaction between two nearby objects, the plane-wave basis proves convenient for numerical calculations as well as for analytical considerations leading to an optical interpretation of the relevant scattering processes of…
In this work a new expansions of Coulomb potential and interparticle distance, linear term $r_{12}$ are proposed. Except the singularities, the expansions converge to the exact value in the whole coordinate space including the vicinity of…
We consider the enhancement of electric field in the presence of two perfectly conducting spheres. When the two spheres get closer, the electric field have a much larger magnitude compared to the external field in the small gap region…
For the family of model soft Coulomb potentials represented by V(r) = -\frac{Z}{(r^q+\beta^q)^{\frac{1}{q}}}, with the parameters Z>0, \beta>0, q \ge 1, it is shown analytically that the potentials and eigenvalues, E_{\nu\ell}, are…
We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the…
This article illustrates the bound states of Kemmer equation for spin-1 particles. The asymptotic, exact and Coulomb field solutions are obtained by using action principle. In the conclusion the energy spectrum of spin-1 particles moving in…