A rigorous modified Thomas-Fermi theory for atomic systems
Recently Parr and Ghosh [Proc. Natl. Acad. Sci. USA 83, 3577 (1986)] proposed a variant of the classical Thomas-Fermi theory of electrons in an atom. They produced a continuous electron density by introducing the constraint that the integral ∫ℝ3 e-2k|x| Δρ(x)dx exists, where k is determined by the nuclear cusp condition. Their results give improved calculations of ground state electron densities and energies. The present paper provides a rigorous mathematical foundation for the work of Parr and Ghosh and converts their results into theorems. Some generalizations are also obtained. © 1987 American Institute of Physics.
Journal of Mathematical Physics
Goldstein, J., & Rieder, G. (1987). A rigorous modified Thomas-Fermi theory for atomic systems. Journal of Mathematical Physics, 28 (5), 1198-1202. https://doi.org/10.1063/1.527567