类锂体系激发态的精确判据

利用Gálvez Porras关于原子体系电子在核处密度和径向期待值的精确不等式，分别建立了波函数的两套精确判据，它们是独立于能量判据之外的检验波函数精确度的判据. 以类锂体系激发态为研究对象，首先对1s2 3s态的电子在核处密度和径向期待值的上界进行了检查，然后对锂原子1s2 3s态在不同计算方法下由电子在核处密度上界定义的R6值和的上界定义的R4值分别进行了测试，同时还对锂原子双激发态的电子在核处密度和径向期待值的上界进行了检验. 研究表明这两套不等式都可作为原子体系各种能态波函数的精确判据.关键词：电子在核处密度径向期待值全实加关联精确判据

Precise criterion for excited states of the lithiumlike systems

By using the accurate inequalities of the electron density at the nucleus and radial expectation values for atomic systems derived by Gálvez and Porras, we separately construct two sets of precise criterion of the wave function, they are another precise criterion independent of energy to test quality of the wave function. In this paper, we use the excited states of lithiumlike systems as research objects and examine the upper bound of the electron density at the nucleus and radial expectation value <r> for the lithiumlike systems 1s23s state, R6 defined by the upper bounds of the electron density at the nucleus and R4 defined by the upper bounds of radial expectation value <r> for the lithium atom 1s23s state in different calculation methods are also tested，at the same time we check up the upper bound of the electron density at the nucleus and radial expectation value <r> for double excited states of the lithium atom. Research has shown that these two sets of inequalities can be used as precise criterion for wave function of energy states of atomic systems.