%0 Journal Article %T Schrödinger equations for the square root density of an eigenmixture and the square root of an eigendensity spin matrix %+ Institut de Physique Théorique - UMR CNRS 3681 (IPHT) %A Giraud, B.G. %A Moussa, P. %< avec comité de lecture %@ 2469-9985 %J Physical Review C %I American Physical Society %V 82 %P 024301 %8 2010-08 %D 2010 %R 10.1103/PhysRevC.82.024301 %Z PACS Number: 21.60.Jz; 31.15.E-; 71.15.Mb; %Z Physics [physics]/Mathematical Physics [math-ph]Journal articles %X We generalize a “one-eigenstate” version of the density square root theorem to the case of densities coming from eigenmixture density operators. The generalization is of a special interest for the radial density functional theory (RDFT) for nuclei, a consequence of the rotational invariance of the nuclear Hamiltonian; when nuclear ground states have a finite spin, the RDFT uses eigenmixture density operators to simplify predictions of ground-state energies into one-dimensional, radial calculations. We also study Schrödinger equations governing spin eigendensity matrices. %G English %2 https://cea.hal.science/cea-02888112/document %2 https://cea.hal.science/cea-02888112/file/GiMo.pdf %L cea-02888112 %U https://cea.hal.science/cea-02888112 %~ CEA %~ CNRS %~ DSM-IPHT %~ TDS-MACS %~ CEA-DRF %~ GS-MATHEMATIQUES %~ GS-PHYSIQUE