Bound-state position and momentum densities and Slater sum for closed shells in a bare Coulomb field

Some generalizations are effected here of the work of Heilmann and Lieb [Phys. Rev. A 52, 3628 (1995)], who summed the squares of all the normalized bound-state wave functions for the hydrogen atom. One of their main results is shown to be equivalent to a spatial generalization of Kato’s theorem. Their asymptotic evaluation of the above sum for large r is used to obtain a property of the bound-state Slater sum in the high-temperature limit. The corresponding momentum space density is also briefly discussed. © 1996 The American Physical Society.