Remarks on completeness of many-electron Sturmians

A question of completeness of a discrete many-electron Sturmian set proposed in a series of recent publications is considered. It is shown that already in the simplest case of a two-electron system the proposed Sturmians do not form a complete set since the spectrum of a generating eigenproblem is mixed: apart from discrete eigenvalues, with which the discrete Sturmians are associated as corresponding eigenfunctions, the spectrum also contains a continuum part. A peculiar feature of the spectrum found is that infinitely many discrete eigenvalues are embedded in the continuum.