Decay in energy space for the solution of fourth-order Hartree-Fock equations with general non-local interactions

Higher order Schrodinger and Hartree-Fock equations

The domain of validity of the higher-order Schrödinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then the Cauchy theory for higher-order Hartree–Fock equations with bounded and Coulomb potentials is developed. Finally, the existence of associated ground states for the odd-order equations is proved. This renders these quantum equations relevant for...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

Decay Estimates for Fourth Order Wave Equations

may be thought of as a nonlinear beam equation. In this paper we obtain both L-L estimates and space-time integrability estimates on solutions to the linear equation. We also use these estimates to study the local existence and asymptotic behavior of solutions to the nonlinear equation, for nonlinear terms which grow like a certain power of u. The main L-L estimate (Theorem 2.1) states that sol...

Solution of the Hartree - Fock Equations tor Atoms and Diatomic Moleeules with the Finite Element Method

(2) 8;<1>j(r); i = 1, ... ,N mentioned above. A review of the basis sets used in the quantum chemical calculations is given by Wilson [13]. The new developments are the two dimensional fully numerical finite difference method (FDM) [14] and the finite element method (FEM) [15]. It has been shown in both methods that the accuracy to calculate e.g., the total energy is many orders of magnitude be...

∗-compressibility of discrete Hartree-Fock equations

Abstract The Hartree-Fock equations are widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle methods. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equations in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potenti...