Related papers: Coulomb expectation values in $D=3$ and $D=3-2\eps…
We consider one-dimensional regularizations of the Coulomb potential formed by taking a two-dimensional expectation of the Coulomb potential with respect to the Landau states. It is well-known that such functions arises naturally in the…
The Coulomb gauge has at least two advantadges over other gauge choices in that bound states between quarks and studies of confinement are easier to understand in this gauge. However, perturbative calculations, namely Feynman loop…
Schroedinger bound-state problem in D dimensions is considered for a set of central polynomial potentials (containing 2q coupling constants). Its polynomial (harmonic-oscillator-like, quasi-exact, terminating) bound-state solutions of…
The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed:…
We study the effect of spatially dependent mass functions over the solution of the Klein-Gordon equation in the (3+1)-dimensions for spinless bosonic particles where the mixed scalar-vector Coulomb-like field potentials and masses are…
Continuum structures of three short-range interacting particles in a deformed external one-body field are investigated. We use the equivalent $d$-method employing non-integer dimension, $d$, in a spherical calculation with a…
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…
We study the low-energy dynamics in three-dimensional $\mathcal{N}=2$ exceptional gauge theories with matters in a fundamental representation, especially focusing on confinement phases and on a quantum structure of the Coulomb branch in the…
We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon…
The quantum statistical treatment of the Rutherford model, considering matter as a system of point charges (electrons and nuclei) is analyzed. First, in the historical context, the solutions of different fundamental problems, such as the…
The Coulomb interaction between the two protons is included in the calculation of proton-deuteron breakup and of three-body electromagnetic disintegration of ${}^3\mathrm{He}$. The hadron dynamics is based on the purely nucleonic…
We study the D-dimensional Schr\"odinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov-Uvarov method. We obtain energy eigenvalues and the corresponding wave function…
In this work, we discuss the relativistic Landau-He-McKellar-Wilkens quantization and relativistic bound states solutions for a Dirac neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking…
By introducing the scalar potential as modification in the mass term of the Klein-Gordon equation, the influence of a Coulomb-type potential on the Klein-Gordon oscillator is investigated. Relativistic bound states solutions are achieved to…
We discuss the epsilon-method as used in various recent QED bound-state calculations by considering mathematical model examples. Recently obtained results for higher-order self-energy binding corrections at the two-loop level are reviewed.…
We propose a novel method for calculating resonances in three-body Coulombic systems. The method is based on the solution of the set of Faddeev and Lippmann-Schwinger integral equations, which are designed for solving the three-body Coulomb…
We study systems of three bosons bound by a long-range interaction supplemented by a short-range potential of variable strength. This generalizes the usual two-body exotic atoms where the Coulomb interaction is modified by nuclear forces at…
The leading-order two-loop vacuum-polarization potential, linear in the Coulomb field of a nucleus, was first derived in the seminal 1955 work of K\"all\'en-Sabry. The higher-order two-loop vacuum-polarization corrections, however, have…
With the shrinking of dimensionality, Coulomb interactions play a distinct role in two-dimensional (2D) semiconductors owing to the reduced dielectric screening in the out-of-plane direction. Apart from dielectric screening, free charge…
A new dimensional scaling method for the calculation of excited states of multielectron atoms is introduced. By including the principle and orbital quantum numbers in the dimension parameter, we obtain an energy expression for excited…