Geodesic
Single-electron Schr\"odinger equation for many-electron systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 3, pp. 450-463

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We show that under certain conditions, an electron of a many-electron system can be described by the Schrödinger equation with a local Hamiltonian. The square root of the electron density plays the role of the wave function, and the interaction with other electrons is taken into account by averaging with the exact conditional probability. The equation dictates a redefinition of the ionization energy, which is tested with the examples of the hydrogen molecule and two-electron atoms. 
@article{TMF_1999_121_3_a7,
     author = {L. P. Ginzburg},
     title = {Single-electron {Schr\"odinger} equation for many-electron systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {450--463},
     publisher = {mathdoc},
     volume = {121},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_121_3_a7/}
}
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L. P. Ginzburg. Single-electron Schr\"odinger equation for many-electron systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 121 (1999) no. 3, pp. 450-463. http://geodesic.mathdoc.fr/item/TMF_1999_121_3_a7/