Related papers: Ewald sums for Yukawa potentials in quasi-two-dime…
Ewald summation is an efficient method for computing the periodic sums that appear when considering the Green's functions of Stokes flow together with periodic boundary conditions. We show how Ewald summation, and accompanying truncation…
Approximate analytical solutions of a two-term potential are studied for the relativistic wave equations, namely, for the Klein-Gordon and Dirac equations. The results are obtained by solving of a Riemann-type equation whose solution can be…
This thesis concerns the correlation structure of interacting Fermi gases on a torus in the mean-field regime. A bosonization method in the spirit of Sawada is developed to analyze the system, and is applied to obtain an upper bound for the…
In this paper we solve analytically Dirac equation for Eckart plus Hulthen potentials with Coulomb-like and Yukawa-like tensor interaction in the presence of Spin and Pseudo-spin Symmetry for any k number. The Parametric Nikiforov-Uvarov…
We present a general approach for the solution of the three-body problem for a general interaction, and apply it to the case of the Coulomb interaction. This approach is exact, simple and fast. It makes use of integral equations derived…
The Sommerfeld factor for arbitrary partial wave processes is derived in the non-relativistic limit. The s-wave and p-wave numerical results are presented for the case of Yukawa interactions. An approximate analytic expression is also found…
Potentials play an important role in solving boundary value problems for elliptic equations. In the middle of the last century, a potential theory was constructed for a two-dimensional elliptic equation with one singular coefficient. In the…
In this paper, we investigate the approximate analytical bound states with a linear combination of two diatomic molecule potentials, Yukawa and four parameters potentials, within the framework of the path integral formalism. With the help…
We investigate the one-dimensional Coulomb potential with application to a class of quasirelativistic systems, so-called Dirac-Weyl materials, described by matrix Hamiltonians. We obtain the exact solution of the shifted and truncated…
Recent progress in the nonperturbative solution of (3+1)-dimensional Yukawa theory and quantum electrodynamics (QED) and (1+1)-dimensional super Yang-Mills (SYM) theory will be summarized. The work on Yukawa theory has been extended to…
In this paper we study pattern formation for a physical local/nonlocal interaction functional where the local attractive term is given by the $1$-perimeter and the nonlocal repulsive term is the Yukawa (or screened Coulomb) potential. This…
The third moment frequency sum rule for the density-density correlation function is rederived in the presence of Umklapp processes. Upper and lower bounds on the electron-electron Coulomb energy are derived in two-dimensional and…
A new approximation formalism is applied to study the bound states of the Hellmann potential, which represents the superposition of the attractive Coulomb potential $-a/r$ and the Yukawa potential $b\exp (-\delta r)/r$ of arbitrary strength…
In recent work a general solution of the Ornstein Zernike equation for a general Yukawa closure for a single component fluid was found. Because of the complexity of the equations a simplifying assumption was made, namely that the main…
A rigorous proof for convergence of the Wolf method for calculating electrostatic energy of a periodic lattice is presented. In particular, we show that for an arbitrary lattice of unit cells, the lattice sum obtained via Wolf method…
We report the implementation of effective QED potentials for all-electron 4-component relativistic molecular calculations using the DIRAC code. The potentials are also available for 2-component calculations, proper picture-change being…
In this paper, we employ methods of contour integration and residue calculus to investigate the parity of two classes of cyclotomic Euler-type sums. One class involves products of cyclotomic harmonic numbers, while the other involves…
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schr\"odinger models with energy-dependent potentials, conventional Schr\"odinger…
In this paper, we establish the analysis of noncommutative Yukawa theory, encompassing neutral and charged scalar fields. We approach the analysis by considering carefully the derivation of the respective effective actions. Hence, based on…
We present a generalization of the Fefferman-de la Llave decomposition of the Coulomb potential to quite arbitrary radial functions $V$ on $R^n$ going to zero at infinity. This generalized decomposition can be used to extend previous…