Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Spectral Method

Abstract

The problem of the structure of hydrogen atom is the most important problem in the field of atomic and molecular structure. Bahr’s treatment of the hydrogen atom marked the beginning of the old quantum theory of atomic structure, and wave mechanics had its inception in Schrodinger ‘s first paper, in which he gave the solution of the wave equation for the hydrogen atom. Since the most differential equations concerning physical phenomenon could not be solved by analytical method hence, the solutions of the wave equation are based on polynomial (series) methods. Even if we use series method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., 砿嫗嫗 + 岫に兼継h貸態 − 糠態捲態岻砿 = ど,