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

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      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

       

      Vikram Soni1

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

       
  • Pramana – Journal of Physics | News

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