Related papers: Simple high-accuracy method for solving bound-stat…
We develop continuous-stage Runge-Kutta-Nystr\"{o}m (csRKN) methods for solving second order ordinary differential equations (ODEs) in this paper. The second order ODEs are commonly encountered in various fields and some of them can be…
A common quark potential that captures the essential traits of the QCD quark-gluon dynamics is expected to (i) interpolate between a Coulomb-like potential (associated with one-gluon exchange) and the infinite wall potential (associated…
This paper introduces planewave density interpolation methods for the regularization of weakly singular, strongly singular, hypersingular and nearly singular integral kernels present in 3D Helmholtz surface layer potentials and associated…
We present a new reciprocal space analytical method to cutoff the long range interactions in supercell calculations for systems that are infinite and periodic in 1 or 2 dimensions, extending previous works for finite systems. The proposed…
We solved the radial Schr"odinger equation analytically using the Exact Quantization Rule approach to obtain the energy eigenvalues with the Extended Cornell potential ECP. The present results are applied for calculating the mass spectra of…
We show that one can obtain naturally the Cornell confining potential from the spontaneous symmetry breaking of scale invariance in gauge theory. At the classical level a confining force is obtained and at the quantum level, using a gauge…
The local moment approach is extended to the orbitally-degenerate [SU(2N)] Anderson impurity model (AIM). Single-particle dynamics are obtained over the full range of energy scales, focussing here on particle-hole symmetry in the strongly…
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…
Objective: The subtraction approach is known for being a theoretically-rigorous and accurate technique for solving the forward problem in electroencephalography by means of the finite element method. One key aspect of this approach consists…
The newly developed single trajectory quadrature method is applied to solve the ground state quantum wave function for Coulomb plus linear potential. The general analytic expressions of the energy and wave function for the ground state are…
The Dyson-Schwinger equations arising from minimizing the vacuum energy density in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge are solved numerically. A new solution is presented which gives rise to a strictly linearly…
Using the formalism of generalized fractional derivatives, a two-dimensional non-relativistic meson system is studied. The mesons are interacting by a Cornell potential. The system is formulated in the domain of the symplectic quantum…
In this report, we present a discussion about different frameworks to perform precise higher-order computations for high-energy physics. These approaches implement novel strategies to deal with infrared and ultraviolet singularities in…
We discuss, in a pedagogical way, how to solve for relativistic wave functions from the radial Dirac equations. After an brief introduction, in Section II we solve the equations for a linear Lorentz scalar potential, V_s(r), that provides…
Using the method of the "exact discretization" of the Schr\"odinger equation, we propose a particular discretized version of the N=2 Supersymmetric Quantum Mechanics. After defining the corresponding shape invariance condition, we show that…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
We use the Tridiagonal Representation Approach (TRA) to obtain exact bound states solution (energy spectrum and wavefunction) of the Schr\"odinger equation for a three-parameter short-range potential with 1/r, 1/r^2 and 1/r^3 singularities…
We present a novel numerical routine (oscode) with a C++ and Python interface for the efficient solution of one-dimensional, second-order, ordinary differential equations with rapidly oscillating solutions. The method is based on a…
We investigate the quantum behavior of a quark-antiquark bound system under the influence of a magnetic field within the symplectic formulation of quantum mechanics. Employing a perturbative approach, we obtain the ground and first excited…
We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the…