A simple extension of a method by Calogero and Marchioro for constructing lower bound problems for ground states of systems of indistinguishable particles is applied to atomic systems. Their method is extended to yield an improved lower bound problem, which raises the ground-state estimate and yields nontrivial lower bounds to excited states that were previously inaccessible by their method. Rigorous upper bounds to atomic ionization energies are also derived. (C) 2000 John Wiley & Sons, Inc. [References: 18]
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机译：由Calogero和Marchioro建立的方法的简单扩展，该方法用于为不可区分的粒子系统的基态构造下界问题，该方法已应用于原子系统。他们的方法得到扩展，产生了一个改进的下界问题，该问题提高了基态估计值，并产生了以前用他们的方法无法访问的激发态的非平凡下界。还得出了原子电离能的严格上限。 （C）2000 John Wiley＆Sons，Inc. [参考：18]
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