Moroz, Irene M.; Penrose, Roger; Tod, Paul Spherically-symmetric solutions of the Schrödinger-Newton equations. (English) Zbl 0936.83037 Classical Quantum Gravity 15, No. 9, 2733-2742 (1998). The goal of the authors is to understand the quantum state reduction as a gravitational phenomenon in the framework of the Newtonian gravitation. For this they consider the Schrödinger-Newton equations. This is a coupled system consisting of the Schrödinger equation for a particle moving in its own gravitational field, where this is generated by its own probability density via the Poisson equation. Using both numerical and analytic investigations, the authors find a discrete family of spherically-symmetric solutions of these equations, everywhere regular, and with normalizable wavefunctions. The solutions are labelled by the non-negative integers, the \(n\)th solution having \(n\) zeros in the wavefunction. These solutions are the only globally defined spherically-symmetric solutions. Reviewer: D.V.Alekseevsky (Moskva) Cited in 3 ReviewsCited in 132 Documents MSC: 83C99 General relativity 81T20 Quantum field theory on curved space or space-time backgrounds 83E05 Geometrodynamics and the holographic principle Keywords:Schrödinger-Newton equations; Newton gravity; quantum state reduction PDF BibTeX XML Cite \textit{I. M. Moroz} et al., Classical Quantum Gravity 15, No. 9, 2733--2742 (1998; Zbl 0936.83037) Full Text: DOI OpenURL