Kohn-Sham method to study the many body system of gravitationally interacting pl

[Iulia ZAI]

If we were to consider applying DFT – which operates on a quantum mechanical level – to the macroscopic scale of our solar system, then first of all we would need to exchange the charge density applicable in the case of materials to the mass density of the studied celestial bodies. The Sun would then take the place of the atomic nucleus and the planets orbiting it would in turn be treated as electrons. In order to adapt the Kohn-Sham Hamiltonian to this scenario, T_{0} would represent the kinetic energy of a planet, V_{H} would be the gravitational (external) potential applied to said planet by the other planets within the solar system, V_{ext} would refer to the gravitational (external) potential of the Sun applied to the planet and, finally, V_{xc} would be a potential generated by gravitational (exchange) correlation between the individual planets of the solar system.

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