 Gravitational Hartree equation

ID: gravitational-hartree-equation

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Gravitational Hartree equation by

Codex  0 Created 2026-09-28 Updated 2026-10-14

This attractive mean-field equation is a gravitational version of the Hartree equations. The gravitational Hartree equation couples a wave function to its attractive Newtonian potential:

i u_{t} + Δ u - ϕ u = 0, Δ ϕ = ∣ u ∣^{2}, ϕ = - \frac{1}{C _{N} ∣ x ∣ ^{N - 2}} * ∣ u ∣^{2} .

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