Related papers: Radial Kohn-Sham problem via integral-equation app…
We propose a hybrid quantum-classical algorithm for solving the time-independent Schr\"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes…
The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistence searching method involves…
We consider the Schr\"odinger equation with a general interaction term, which is localized in space, for radially symmetric initial data in $n$ dimensions, $n\geq5$. The interaction term may be space-time dependent and nonlinear. Assuming…
The Qprop package is presented. Qprop has been developed to study laser-atom interaction in the nonperturbative regime where nonlinear phenomena such as above-threshold ionization, high order harmonic generation, and dynamic stabilization…
The Schroedinger equation is solved for an A-nucleon system using an expansion of the wave function in nonsymmetrized hyperspherical harmonics. Our approach is both an extension and a modification of the formalism developed by Gattobigio et…
The rectangular collocation approach makes it possible to solve the Schr\"odinger equation with basis functions that do not have amplitude in all regions in which wavefunctions have significant amplitude. Collocation points can be…
In this paper, a novel $h$-adaptive isogeometric solver utilizing high-order hierarchical splines is proposed to solve the all-electron Kohn--Sham equation. In virtue of the smooth nature of Kohn--Sham wavefunctions across the domain,…
The Hyperspherical Harmonics (HH) method is one of the most accurate techniques to solve the quantum mechanical problem for nuclear systems with $A\le 4$. In particular, by applying the Rayleigh-Ritz or Kohn variational principle, both…
The implementation of the orbital minimization method (OMM) for solving the self-consistent Kohn-Sham (KS) problem for electronic structure calculations in a basis of non-orthogonal numerical atomic orbitals of finite-range is reported. We…
Recently, the Asymptotic Iteration Method (AIM) was used to calculate the energy spectrum for a short rang three parameter central potential which was introduced by H. Bahlouli and A. D. Alhaidari. The S-orbital wave solution of the…
In the harmonic oscillator representation, the Schrodinger equation has a form of a set of infinite number of algebraical equations which are labeled by the radial quantum number "n". It is shown that at n>>1 these equations are…
We study the energy spectrum of the two-electron spherical parabolic quantum dot using the exact Schroedinger, the Hartree-Fock, and the Kohn-Sham equations. The results obtained by applying the shifted-1/N method are compared with those…
A method for the fast and accurate solution of the radiative transfer equation in plane-parallel media with coherent isotropic scattering is presented. This largely analytical approach uses the formalism of meromorphic functions in order to…
We address the problem of bounding rigorously the errors in the numerical solution of the Kohn-Sham equations due to (i) the finiteness of the basis set, (ii) the convergence thresholds in iterative procedures, (iii) the propagation of…
We study the Kohn-Sham scheme for the calculation of the steady state linear response to a harmonic perturbation that is turned on adiabatically. Although in general the exact time dependent exchange-correlation potential cannot be…
A robust and general solver for the radial Schr\"odinger, Dirac, and Kohn--Sham equations is presented. The formulation admits general potentials and meshes: uniform, exponential, or other defined by nodal distribution and derivative…
A new non-perturbative approach is proposed to solve time-independent Schr\"{o}dinger equations in quantum mechanics and chromodynamics (QCD). It is based on the homotopy analysis method (HAM), which was developed by the author for highly…
In this work, we consider the inverse scattering transform and multi-solition solutions of the sextic nonlinear Schr\"{o}dinger equation. The Jost functions of spectrum problem are derived directly, and the scattering data with $t=0$ are…
We outline a rigorous method which can be used to solve the many-body Schroedinger equation for a Coulomb interacting electronic system in an external classical magnetic field as well as a quantized electromagnetic field. Effects of the…
We define symmetries in non-relativistic quantum electrodynamics, which have the physical interpretation of rotation, parity and time reversal symmetry. We collect transformation properties related to these symmetries in Fock space…