相关论文: Linear Scaling Solution of the Coulomb problem usi…
The scattering problem for two particles interacting via the Coulomb potential is examined for the case where the potential has a sharp cut-off at some distance. The problem is solved for two complimentary situations, firstly when the…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
After setting up a general model for supersymmetric classical mechanics in more than one dimension we describe systems with centrally symmetric potentials and their Poisson algebra. We then apply this information to the investigation and…
Recent advances in the treatment of scattering of charged composite particles are reviewed. In a first part I report on developments of the theory. Specifically I describe the recent completion of the derivation of the co-ordinate space…
A practical method to solve cut-off Coulomb problems of two-cluster systems in the momentum space is given. When a sharply cut-off Coulomb force with a cut-off radius $\rho$ is introduced at the level of constituent particles, two-cluster…
We introduce an approach, based on the coordinate space Faddeev equations, to solve the quantum mechanical three-body Coulomb problem in the continuum. We apply the approach to compute measured properties of the first two $0^+$ levels in…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…
Using a formulation of quantum mechanics based on orthogonal polynomials in the energy and physical parameters, we present a method that gives the class of potential functions for exactly solvable problems corresponding to a given energy…
Matrix mechanics is an important component of an undergraduate education in quantum mechanics. In this paper we present several examples of the use of matrix mechanics to solve for a number of three dimensional problems involving central…
Coulomb interaction, following an inverse-square force-law, quantifies the amount of force between two stationary and electrically charged particles. The long-range nature of Coulomb interactions poses a major challenge to molecular…
Wave/Schr\"{o}dinger equations with potentials naturally originates from both the quantum physics and the study of nonlinear equations. The distractive Coulomb potential is a quantum mechanical description of distractive Coulomb force…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part, according to variational approach we obtain a…
The Helmholtz equation with variable wavenumbers is challenging to solve numerically due to the pollution effect, which often results in a huge ill-conditioned linear system. In this paper, we present a high-order wavelet Galerkin method to…
Based on the work of Nuttall and Cohen [Phys. Rev. {\bf 188} (1969) 1542] and Resigno et al{} [Phys. Rev. A {\bf 55} (1997) 4253] we present a rigorous formalism for solving the scattering problem for long-range interactions without using…
We show that a difference in time scales of vertical and lateral dynamics permits one to analyze the problem of interacting electrons confined in an axially symmetric three-dimensional potential with a lateral oscillator confinement by…
We present a novel form of relativistic quantum mechanics and demonstrate how to solve it using a recently derived unitary perturbation theory, within partial wave analysis. The theory is tested on a relativistic problem, with two spinless,…
We extend the class of QM problems which permit for quasi-exact solutions. Specifically, we consider planar motion of two interacting charges in a constant uniform magnetic field. While Turbiner and Escobar-Ruiz (2013) addressed the case of…
The charging energy of a quantum dot is measured through the effect of its potential on the conductance of a second dot. This technique allows a measurement of the scaling of the dot's charging energy with the conductance of the tunnel…
We construct a tridiagonal matrix representation for the three dimensions Dirac-Coulomb Hamiltonian that provides for a simple and straightforward relativistic extension of the complex scaling method. Besides the Coulomb interaction,…
Numerical simulations based on electronic structure calculations are finding ever growing applications in many areas of physics. A major limiting factor is however the cubic scaling of the algorithms used. Building on previous work [F. R.…