# Schrödinger–Newton ‘collapse’ of the wavefunction

@article{Meter2011SchrdingerNewtonO, title={Schr{\"o}dinger–Newton ‘collapse’ of the wavefunction}, author={J. V. Meter}, journal={Classical and Quantum Gravity}, year={2011}, volume={28}, pages={215013} }

It has been suggested that the nonlinear Schrodinger–Newton equation might approximate the coupling of quantum mechanics with gravitation, particularly in the context of the Moller–Rosenfeld semiclassical theory. Numerical results for the spherically symmetric, time-dependent, single-particle case are presented, clarifying and extending previous work on the subject. It is found that, for a particle mass greater than 1.14(2/(Gσ))1/3, a wave packet of width σ partially 'collapses' to a… Expand

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#### References

SHOWING 1-10 OF 45 REFERENCES

A numerical study of the Schrödinger-Newton equations

- Mathematics
- 2003

The Schrodinger-Newton (S-N) equations were proposed by Penrose [18] as a model for gravitational collapse of the wave-function. The potential in the Schrodinger equation is the gravity due to the… Expand

Evolution of the Schrödinger--Newton system for a self--gravitating scalar field

- Physics
- 2004

Using numerical techniques, we study the collapse of a scalar field configuration in the Newtonian limit of the spherically symmetric Einstein-Klein-Gordon (EKG) system, which results in the so… Expand

Spherically symmetric solutions of the Schrodinger-Newton equations

- Physics
- 1998

As part of a programme in which quantum state reduction is understood as a gravitational phenomenon, we consider the Schrodinger-Newton equations. For a single particle, this is a coupled system… Expand

Investigation of the time-dependent Schroedinger-Newton equation

- Physics
- 2005

The Schrödinger-Newton equation is a highly non-linear integro-partial differential equation that arises from both the theory of semiclassical gravity of Møller and Rosenfeld and as a possible… Expand

Comments on proposed gravitational modifications of schrödinger dynamics and their experimental implications

- Physics
- 2007

We discuss aspects of gravitational modifications of Schr?dinger dynamics proposed by Di?si and Penrose. We consider first the Di?si?Penrose criterion for gravitationally induced state vector… Expand

Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics

- Physics
- 1994

In this book, Robert Wald provides a pedagogical introduction to the formulation of quantum field theory in curved spacetime. He begins with a treatment of the ordinary one-dimensional quantum… Expand

On Gravity's role in Quantum State Reduction

- Physics
- 1996

The stability of a quantum superposition of two different stationary mass distributions is examined, where the perturbing effect of each distribution on the space-time structure is taken into… Expand

Testing spontaneous localization theories with matter-wave interferometry

- Physics
- 2011

It is a basic unresolved question of quantum mechanics whether the Schrodinger equation holds for truly macro- scopic systems. Unitarity then implies that even mea- surement devices or conscious… Expand

Non-linear coupling of quantum theory and classical gravity

- Physics
- 1980

Discusses the possibility that the non-linear evolution proposed earlier for a relativistic quantum field theory may be related to its coupling to a classical gravitational field. Formally, in the… Expand

Scalar field dark matter: Nonspherical collapse and late-time behavior

- Physics
- 2006

Instituto de F´isica y Matem´aticas, Universidad Michoacana de San Nicol´as de Hidalgo. Ediﬁcio C-3,Cd. Universitaria, A. P. 2-82, 58040 Morelia, Michoac´an, M´exico.(Dated: February 5, 2008)We show… Expand