标题： 电子密度平方根无法作为一组完整基函数元素的线性组合展开的不可能性 显示英文标题

标题： The impossibility of expanding the square root of the electron density as a linear combination of elements of a complete set of basis functions

摘要： 在无轨道密度泛函理论（OFDFT）中，存在一个方程用于$\psi = \sqrt n$，即基态电子密度$n$的平方根。 我们证明，$\psi$不能作为一组完整基函数元素的线性组合展开，除非是在一个或两个电子系统的情况下。 这与相同粒子系统的基态情况不同，在这种情况下，基态玻色子密度的平方根可以作为一组完整基函数元素的线性组合展开。 显示英文摘要

摘要： In orbital-free density functional theory (OFDFT), an equation exists for $\psi = \sqrt n$, the square root of the ground state electron density $n$. We show that $\psi$ cannot be expanded as a linear combination of elements of a complete set of basis functions except in the case of one or two electron systems. This is unlike the case for the ground state of a system of identical bosons in which the square root of the ground state bosonic density can have an expansion as a linear combination of elements of a complete set of basis functions.