Related papers: Some recent results on contact or point supported …
Using one-range addition theorems for noninteger n Slater type orbitals and Coulomb-Yukawa like correlated interaction potentials with noninteger indices obtained by the author with the help of complete orthonormal sets of exponential type…
We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric attractive cusp potential. The components of the spinor solution are expressed in terms of Whittaker functions. We compute the bound states…
We optimize the first and second intrinsic hyperpolarizabilities for a 1D piecewise linear potential dressed with Dirac delta functions for $N$ non-interacting electrons. The optimized values fall rapidly for $N>1$, but approach constant…
This paper is devoted to the approximation of two and three-dimensional Dirac operators $H_{\widetilde{V} \delta_\Sigma}$ with combinations of electrostatic and Lorentz scalar $\delta$-shell interactions in the norm resolvent sense. Relying…
We extend previous work on the vacuum energy of a massless scalar field in the presence of singular potentials. We consider a single sphere denoted by the so-called "delta-delta prime" interaction. Contrary to the Dirac delta potential, we…
When studying (or teaching) classical electromagnetism, one is bound to deal with the electric field of an ideal electric dipole, as well as its magnetic counterpart. A careful analysis then reveals that each of those fields must include,…
We examine the bound state solutions of the Dirac equation under the spin and pseudospin symmetries for a new suggested combined potential, Hulten plus a class of Yukawa potential including a Coulomb-like tensor interaction. An improved…
Approximate analytical solutions of the Dirac equation are obtained for the Yukawa potential plus a tensor interaction with any $\kappa$-value for the cases having the Dirac equation pseudospin and spin symmetry. The potential describing…
After reviewing the algebraic derivation of the Doppler factor in the Lienard-Wiechert potentials of an electrically charged point particle, we conclude that the Dirac delta function used in electrodynamics must be the one obeying the weak…
We provide a successful fit for proton-neutron scattering below pion production threshold up to LAB energies of 350 MeV. We use seven high-quality fits based on potentials with different forms as a measure of the systematic uncertainty. We…
In this research, we present a Python-based solution designed to simulate a one-dimensional quantum system that incorporates multiple Dirac $\delta -$% potentials. The primary aim of this research is to investigate the scattering problem…
The interacting electron and hole in transition-metal dichalcogenides is considered. For investigation of the interaction between electron and hole we obtain the Bethe-Salpeter equation for two interacting Dirac particles. The dependence of…
We constrain general Dirac neutrino interactions based on the Standard Model Effective Field Theory framework extended with right-handed neutrinos $N$ (SMNEFT) using deep inelastic and coherent elastic neutrino scattering, nuclear beta…
This paper is concerned with the spectral analysis of a Hamiltonian with a $\delta$-interaction supported along a broken line with angle $\theta$. The bound states with energy slightly below the threshold of the essential spectrum are…
We discuss the potential scattering on the noncompact star graph. The Schr\"{o}dinger operator with the short-range potential localizing in a neighborhood of the graph vertex is considered. We study the asymptotic behavior the corresponding…
In this work, we study the probability distribution for the force and potential energy of a test particle interacting with $N$ point random sources in the limit $N\rightarrow\infty$. The interaction is given by a central potential…
The main progress in the field of nucleon-nucleon (NN) potentials, which we have seen in recent years, is the construction of some very quantitative (high-quality/high-precision) NN potentials. These potentials will serve as excellent input…
The one-dimensional Dirac operator with a singular interaction term which is formally given by $A\otimes|\delta_0\rangle\langle\delta_0|$, where $A$ is an arbitrary $2\times 2$ matrix and $\delta_0$ stands for the Dirac distribution, is…
We construct a four-parameter point-interaction for a non-relativistic particle moving on a line as the limit of a short range interaction with range tending toward zero. For particular choices of the parameters, we can obtain a…
Dirac equation for a charged particle in static electromagnetic field is written for special cases of spherically symmetric potentials. Besides the well known Dirac-Coulomb and Dirac-Oscillator potentials, we obtain a relativistic version…