Convergence of Green Iterations for Schrödinger Equations
نویسندگان
چکیده
For a time-independent Schrödinger equation with Hamiltonian operator H = −∆ + V on L(R ) we call Gz = RzV , the Green function operator, where Rz is the resolvent of −∆. We consider an iteration scheme that is based on the operator Gz. Under standard conditions on the potential V , which include the Coulomb interaction, we prove the convergence of the iteration to the ground state energy and eigenfunction when N = 1 or 2.
منابع مشابه
A STABLE COUPLED NEWTON'S ITERATION FOR THE MATRIX INVERSE $P$-TH ROOT
The computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. It is possible toapproximate the matrix inverse pth roots by exploiting a specialized version of New-ton's method, but previous researchers have mentioned that some iter...
متن کاملPreconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation
Introduction Fractional differential equations (FDEs) have attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme may be a good approach, particularly, the schemes in numerical linear algebra for solving ...
متن کاملA Composite Finite Difference Scheme for Subsonic Transonic Flows (RESEARCH NOTE).
This paper presents a simple and computationally-efficient algorithm for solving steady two-dimensional subsonic and transonic compressible flow over an airfoil. This work uses an interactive viscous-inviscid solution by incorporating the viscous effects in a thin shear-layer. Boundary-layer approximation reduces the Navier-Stokes equations to a parabolic set of coupled, non-linear partial diff...
متن کاملStrong Convergence of the Iterations of Quasi $phi$-nonexpansive Mappings and its Applications in Banach Spaces
In this paper, we study the iterations of quasi $phi$-nonexpansive mappings and its applications in Banach spaces. At the first, we prove strong convergence of the sequence generated by the hybrid proximal point method to a common fixed point of a family of quasi $phi$-nonexpansive mappings. Then, we give applications of our main results in equilibrium problems.
متن کامل