On the matrix factorization of many-particle Coulomb Hamiltonians

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.