Related papers: Coulomb expectation values in $D=3$ and $D=3-2\eps…
We present perturbative energy eigenvalues (up to second order) of Coulomb- and harmonic oscillator-type fields within a perturbation scheme. We have the required unperturbed eigenvalues ($E_{n}^{(0)}$) analytically obtained by using…
We prove a new lower bound on the indirect Coulomb energy in two dimensional quantum mechanics in terms of the single particle density of the system. The new universal lower bound is an alternative to the Lieb--Solovej--Yngvason bound with…
In this work, we analyze the noncommutative three-dimensional Coulomb potential problem. For this purpose, we used the Kustaanheimo-Stiefel mapping to write the Schr\"odinger equation for Coulomb potential in a solvable way. Then, the…
We develop a calculational scheme in Coulomb and temporal gauge that respects gauge invariance and is most easily applied to the infrared asymptotic region of QCD. It resembles the Dyson-Schwinger equations of Euclidean quantum field theory…
We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb operator in a suitable complete square integrable basis. Orthogonal polynomials techniques along with Darboux method are used to obtain the bound states energy…
In this article, we investigate the bound state solution of the Klein Gordon equation under mixed vector and scalar coupling of an energy-dependent deformed Hulth\'en potential in D-dimensions. We obtain a transcendental equation after we…
Analytic and approximate solutions for the energy eigenvalues generated by a confined softcore Coulomb potentials of the form a/(r+\beta) in d>1 dimensions are constructed. The confinement is effected by linear and harmonic-oscillator…
With the aim of progressing toward a practical implementation of an effective quantum-electrodynamics (QED) theory of atoms and molecules, which includes the effects of vacuum polarization through the creation of virtual electron-positron…
Consider the free energy of a $d$-dimensional gas in canonical equilibrium under pairwise repulsive interaction and global confinement, in presence of a volume constraint. When the volume of the gas is forced away from its typical value,…
We report the potential energy curve, the diagonal Born-Oppenheimer, non-adiabatic mass, relativistic, and leading-order QED corrections for the ground electronic state of the helium dimer cation; the higher-order QED and finite-nuclear…
The contour integrals, occurring in the arbitrary-order phase-integral quantization conditions given in a previous paper, are in the first- and third-order approximations expressed in terms of complete elliptic integrals in the case that…
We prove a Central Limit Theorem for the linear statistics of two-dimensional Coulomb gases, with arbitrary inverse temperature and general confining potential, at the macroscopic and mesoscopic scales and possibly near the boundary of the…
The static Coulomb potential of Quantum Electrodynamics (QED) is calculated in the presence of a strong magnetic field in the lowest Landau level (LLL) approximation using two different methods. First, the vacuum expectation value of the…
A novel method for calculating resonances in three-body Coulombic systems is proposed. The Faddeev-Merkuriev integral equations are solved by applying the Coulomb-Sturmian separable expansion method. The $e^- e^+ e^-$ S-state resonances up…
We revisit the derivation of the covariant two-body scalar-fermion equation with a Coulomb interaction, presented in a previous paper. We show that it can be given the formal aspect of a Dirac equation, but for the fact that the eigenvalue…
By the use of the variational method with exponential trial functions the upper and lower bounds of energy are calculated for a number of non-relativistic three-body Coulomb and nuclear systems. The formulas for calculation of upper and…
Based on a three-potential formalism we propose mathematically well-behaved Faddeev-type integral equations for the atomic three-body problem and descibe their solutions in Coulomb-Sturmian space representation. Although the system contains…
This paper discusses an attempt to develop a mathematically rigorous theory of Quantum Electrodynamics (QED). It deviates from the standard version of QED mainly in two aspects: it is assumed that the Coulomb forces are carried by…
We introduce the Dunkl--Klein--Gordon (DKG) equation in 2D by changing the standard partial derivatives by the Dunkl derivatives in the standard Klein--Gordon (KG) equation. We show that the generalization with Dunkl derivative of the…
Quantum confinement is studied by numerically solving time-dependent Schr\"odinger equation. An imaginary-time evolution technique is employed in conjunction with the minimization of an expectation value, to reach the global minimum.…