Related papers: New and efficient method for solving the eigenvalu…
A local and parallel algorithm based on the multilevel discretization is proposed in this paper to solve the eigenvalue problem by the finite element method. With this new scheme, solving the eigenvalue problem in the finest grid is…
Motivated by the recently proposed parallel orbital-updating approach in real space method, we propose a parallel orbital-updating based plane-wave basis method for electronic structure calculations, for solving the corresponding eigenvalue…
The goal of this paper is to calculate bound, resonant and scattering states in the coupled-channel formalism without relying on the boundary conditions at large distances. The coupled-channel solution is expanded in eigenchannel bases i.e.…
We make use of a recently developed method to, not only obtain the exactly known eigenstates and eigenvalues of a number of quasi-exactly solvable Hamiltonians, but also construct a convergent approximation scheme for locating those levels,…
We present a new approach to real-space multiple-scattering theory for molecules and clusters, based on the two-potential (distorted-wave) Lippmann-Schwinger equation formalism. Our approach uses a recently developed form [D. L. Foulis,…
We extend the conforming virtual element method to the numerical resolution of eigenvalue problems with potential terms on a polytopal mesh. An important application is that of the Schrodinger equation with a pseudopotential term. This…
We use the factorization method to find the exact eigenvalues and eigenfunctions for a particle in a box with the delta function potential $V(x)=\lambda\delta(x-x_{0})$. We show that the presence of the potential results in the…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
We propose a new method for computing the eigenvalue decomposition of a dense real normal matrix $A$ through the decomposition of its skew-symmetric part. The method relies on algorithms that are known to be efficiently implemented, such as…
Quartic eigenvalue problem $(\lambda^4 A + \lambda^3 B + \lambda^2C + \lambda D + E)x = \mathbf{0}$ naturally arises e.g. when solving the Orr-Sommerfeld equation in the analysis of the stability of the {Poiseuille} flow, in theoretical…
Generalized eigenvalue problems involving a singular pencil may be very challenging to solve, both with respect to accuracy and efficiency. While Part I presented a rank-completing addition to a singular pencil, we now develop two…
In the present work, we present different two-body potentials which have oscillatory shapes with magnetic interactions. The eigenvalues and eigenfunctions are obtained for one of those problems using Nikiforov-Uvarov method.
Extending the supersymmetric method proposed by Tkachuk to the complex domain, we obtain general expressions for superpotentials allowing generation of quasi-exactly solvable PT-symmetric potentials with two known real eigenvalues (the…
Shell corrections of the finite deformed Woods-Saxon potential are calculated using the Green's function method and the generalized Strutinsky smoothing procedure. They are compared with the results of the standard prescription which are…
We investigate the scattering of scalar plane waves in two dimensions by a heterogeneous layer that is periodic in the direction parallel to its boundary. On describing the layer as a union of periodic laminae, we develop a solution of the…
This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables…
Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…
The Lagrange mesh method is a very simple procedure to accurately solve eigenvalue problems starting from a given nonrelativistic or semirelativistic two-body Hamiltonian with local or nonlocal potential. We show in this work that it can be…
Herein, we present analytical solutions for the electronic energy eigenvalues of the hydrogen molecular ion H2+, namely the one-electron two-fixed-center problem. These are given for the homonuclear case for the countable infinity of…
We focus on a recently developed generalized pseudospectral method for accurate, efficient treatment of certain central potentials of interest in various branches in quantum mechanics, usually having singularity. Essentially this allows…