Related papers: Radial Kohn-Sham problem via integral-equation app…

An effective approach for solving the three-dimensional Dirac equation for spherically symmetric local interactions, which we have introduced recently, is reviewed and consolidated. The merit of the approach is in producing Schrodinger-like…

Both the no-core shell model and the effective interaction hyperspherical harmonic approaches are applied to the calculation of different response functions to external electromagnetic probes, using the Lorentz integral transform method.…

We study the spectral correspondence between a particular class of Schrodinger equations and supersymmetric quantum integrable model (QIM). The latter, a quantized version of the Ablowitz-Kaupp-Newell-Segur (AKNS) hierarchy of nonlinear…

The simplest, algebraic quantum-electrodynamical corrections, due to the double-negative energy subspace and instantaneous interactions, are computed to the no-pair energy of two-spin-1/2-fermion systems. Numerical results are reported for…

In many applications to finite Fermi-systems, the pairing problem has to be treated exactly. We suggest a numerical method of exact solution based on SU(2) quasispin algebras and demonstrate its simplicity and practicality. We show that the…

An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…

Nonlocality in the scattering potential leads to an integro-differential equation.In this equation nonlocality enters through an integral over the nonlocal potential kernel. The resulting Schroedinger equation is usually handled by…

We describe a rapidly converging algorithm for solving the Kohn--Sham equations and equations of similar structure that appear frequently in calculations of the structure of inhomogeneous electronic many--body systems. The algorithm has its…

In this article, we derive fully guaranteed error bounds for the energy of convex nonlinear mean-field models. These results apply in particular to Kohn-Sham equations with convex density functionals, which includes the reduced Hartree-Fock…

We introduce a new computational approach for femtosecond pulse propagation in the transparency region of gases that permits full resolution in three space dimensions plus time while fully incorporating quantum coherent effects such as…

The time-dependent one-dimensional nonlinear Schr\"odinger equation (NLSE) is solved numerically by a hybrid pseudospectral-variational quantum algorithm that connects a pseudospectral step for the Hamiltonian term with a variational step…

We derive solutions of the Schr\"{o}dinger equation for the isotropic van der Waals interaction in a symmetric harmonic trap, with the recent approach [arXiv:2207.09377 (2022)] to handle the multi-scale long-range potential. Asymptotic…

In this paper, a novel adaptive finite element method is proposed to solve the Kohn-Sham equation based on the moving mesh (nonnested mesh) adaptive technique and the augmented subspace method. Different from the classical self-consistent…

In this article we analyze the behavior of a non-relativistic spinless particle near the event horizon of a Schwarzschild-like black hole. In this way, the Schr\"odinger covariant equation that describes the particle is obtained from the…

Predictivity of the Kohn-Sham approach to dynamical problems, when regarded as an initial value problem in a time-dependent density functional framework, is analysed for a class of models for which the argument devised in the work of Maitra…

In this work, we consider solutions to (fully nonlinear) parabolic integro-differential equations with integrable interaction kernels. A typical equation would be that obtained by starting with, for $s\in(0,1)$, the $s$-fractional heat…

We develop an advanced method of solving homogeneous and inhomogeneous Bethe-Salpeter equations by using the expansion over the complete set of 4-dimensional spherical harmonics. We solve Bethe-Salpeter equations for bound and scattering…

Seeking for a relativistic generalisation of the non-relativistic Schroedinger equation, one very soon arrives at equations with a square-root operator by having applied the quantum mechanical correspondence principle to the formula of…

Kohn-Sham density functional theory calculations using conventional diagonalization based methods become increasingly expensive as temperature increases due to the need to compute increasing numbers of partially occupied states. We present…

In this paper it is shown how to solve numerically eigenvalue problems associated to second order linear ordinary differential equations, containing also terms which depend on the variable. A didactic presentation of the Numerov Method is…