• Planck scale physics of the single-particle Schrödinger equation with gravitational self-interaction

• # Fulltext

Permanent link:
https://www.ias.ac.in/article/fulltext/pram/059/02/0375-0383

• # Keywords

Quantum mechanics; gravitation; state reduction

• # 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 ‘massdensity’ that enters this term is given by m|ψ($$\overrightarrow r$$,t)|2, where ψ($$\overrightarrow r$$,t) is the wave function and m is the mass of the particle. This leads to a nonlinear equation, the ‘Newton-Schrödinger’ equation, which has been found to possess stationary self-bound solutions, whose energy can be determined using an asymptotic method. We find that such a particle strongly violates the superposition principle and becomes a black hole as its mass approaches the Planck mass.

• # Author Affiliations

1. National Physical Laboratory, K.S. Krishnan Marg, New Delhi - 110 016, India

• # Pramana – Journal of Physics

Volume 94, 2020
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Posted on July 25, 2019

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