On the matrix factorization of many-particle Coulomb Hamiltonians

TL;DR

This paper demonstrates that many-particle Coulomb Hamiltonians can always be factorized, enabling analytical formulas for bound state spectra of complex atomic systems, similar to the hydrogen atom's Bohr formula.

Contribution

It introduces a universal factorization method for many-particle Coulomb Hamiltonians, leading to explicit spectral formulas for complex atomic systems.

Findings

Factorization of Coulomb Hamiltonians is always possible.

Analytical formulas for bound states are derived for arbitrary many-particle systems.

Formulas resemble Bohr's formula for hydrogen, extending its applicability.

Abstract

It is shown that the Coulomb many-particle Hamiltonians are always factorized. This fact can be used to obtain the closed analytical formula(s) for the bound state spectra of an arbitrary many-particle Coulomb system. For few- and many-electron atoms and ions these formulas are similar in some sense to the Bohr's formula which describes the bound state spectra of the hydrogen atom.