Numerical solutions of the Schrödinger equation for the ground lithium by the finite element method

摘要

In the present paper, the authors transfers the nine-dimensional Schrödinger equation of the ground lithium into a six-dimensional partial differential equation. A six-dimensional variational formulation is also derived from the weak energy equation. A kind of six-dimensional finite element methods are constructed to solve the transferred energy equation. With very coarse mesh, the authors get highly precise approximate eigenvalue. The relative error of approximate eigenvalue is order of 10−5 in atomic unit.