Numerical Solution of the Perturbed Harmonic Oscillator Equation and the Hartreefock Many-Electron Equations by Use of Green's Function

摘要

The numerical solution of the perturbed harmonic oscillator equation and the Hartree-Fock equations by use of Green's Function was demonstrated to be a powerful method. The given quantum mechanical differential equation is transformed into an integral equation by means of Green's Function. Even if the integral equation is nonlinear or has an unsymmetric kernel, or both, the integral equation is easily solved numerically by an iterative scheme. When the integral equation is linear and has a symmetric kernel, the integral equation may be solved for the unknown eigenvalues and eigenfunctions by diagonalization of the kernel by the method of Jacobi. The boundary conditions of the physical problem are built into the integral equation by the Green's Function, and need not be forced during the iteration scheme as in the method of Numerov.