Matrix mechanics for actual atoms and molecules

TL;DR

This paper develops a matrix mechanics approach using hyperspherical coordinates to analyze the bound state spectra of atoms, ions, and molecules, revealing a universal ladder structure that aids in understanding many-electron Coulomb systems.

Contribution

It introduces a novel matrix factorization method for Coulomb Hamiltonians in hyperspherical coordinates, providing new insights into the spectral structure of complex atomic and molecular systems.

Findings

Bound state spectra exhibit a universal ladder structure.

The method effectively characterizes spectra of few- and many-electron systems.

The approach offers a new tool for analyzing Coulomb systems.

Abstract

Matrix mechanics is developed to describe the bound state spectra in few- and many-electron atoms, ions and molecules. Our method is based on the matrix factorization of many-electron (or many-particle) Coulomb Hamiltonians which are written in hyperspherical coordinates. As follows from the results of our study the bound state spectra of many-electron (or many-particle) Coulomb Hamiltonians always have the `ladder' structure and this fundamental fact can be used to determine and investigate the bound states in various few- and many-body Coulomb systems.