Exact density-phase relations have been derived for a three-level independent-particle problem. The density can explicitly be written in terms of the phase functions and cphi and their derivatives. The Euler equation of the density-functional theory has been derived for the ground state of the C atom. The one-body potential V can be obtained from the phase functions and cphi. The differential form of the virial theorem of March and Young [Nucl. Phys. 12, 237 (1959)] has been generalized for particles moving in a common local potential V and having different azimuthal quantum numbers.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics