Planck Scale Physics of the Single Particle Schrödinger Equation with Gravitational Self-Interaction

Abstract

We consider the modification of a single particle Schrödinger equation by the inclusion of an additional gravitational self-potential term which follows from the prescription that the' mass-density'that enters this term is given by $m|\psi (\vec{r},t){|}^2$, where $\psi (\vec{r},t)$ is the wavefunction and $m$ is the mass of the particle. This leads to a nonlinear equation, the ' Newton Schrodinger' equation, which has been found to possess stationary self-bound solutions, whose energy can be determined exactly using an asymptotic method. We find that such a particle strongly violates superposition and becomes a black hole as its mass approaches the Planck mass.

16 pages, Revtex, No figure, Submitted to Physics Letters A

References in corpus (2)

• Gravitation and quantummechanical localization of macroobjects
• Quantum space-time fluctuations and primary state diffusion

Cited by in corpus (4)

• Notes on Certain Newton Gravity Mechanisms of Wave Function Localisation and Decoherence
• Gravitational self-localization in quantum measurement
• The frictional Schrödinger-Newton equation in models of wave function collapse
• Schrodinger-Newton equation with complex Newton constant and induced gravity