![]() ![]() The equation also describes fuzzy dark matter and approximates classical cold dark matter described by the Vlasov–Poisson equation in the limit that the particle mass is large. In this context of classical general relativity it appears as the non-relativistic limit of either the Klein–Gordon equation or the Dirac equation in a curved space-time together with the Einstein field equations. The Schrödinger–Newton equation was first considered by Ruffini and Bonazzola in connection with self-gravitating boson stars. In the latter case it is also referred to in the plural form. It can be written either as a single integro-differential equation or as a coupled system of a Schrödinger and a Poisson equation. ![]() The inclusion of a self-interaction term represents a fundamental alteration of quantum mechanics. The Schrödinger–Newton equation, sometimes referred to as the Newton–Schrödinger or Schrödinger–Poisson equation, is a nonlinear modification of the Schrödinger equation with a Newtonian gravitational potential, where the gravitational potential emerges from the treatment of the wave function as a mass density, including a term that represents interaction of a particle with its own gravitational field. Nonlinear modification of the Schrödinger equation ![]()
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