Remarks On The Standard Hylleraas-Undheim And MacDonald Computation Of Excited States

TL;DR

This paper discusses limitations of the Hylleraas-Undheim and MacDonald method for computing excited states in quantum mechanics, highlighting issues that affect the accuracy of results compared to experimental data.

Contribution

It identifies specific restrictions of the standard method that hinder the quality of excited state calculations.

Findings

Standard solutions have lower quality than the lowest root when sufficiently accurate.

Restrictions prevent reliable comparisons with experimental results.

The paper provides insights into improving excited state computations.

Abstract

For the computation of excited states, the standard solutions of the Schroedinger equation, using higher roots of a secular equation in a finite N-dimensional function space, by the Hylleraas-Undheim and MacDonald theorem, have several restrictions, which render them of lower quality, relative to the lowest root, if the latter is good enough. These deficiencies are reported, that prevent from comparisons with accurate experiments.