Schrödinger--Newton equation with spontaneous wave function collapse
arXiv:2210.15057 · doi:10.3390/quantum4040041
Abstract
Based on the assumption that the standard Schrödinger equation becomes gravitationally modified for massive macroscopic objects, two independent proposals has survived from the nineteen-eighties. The Schrödinger--Newton equation (1984) provides well-localized solitons for free macro-objects but lacks the mechanism how extended wave functions collapse on solitons. The gravity-related stochastic Schrödinger equation (1989) provides the spontaneous collapse but the resulting solitons undergo a tiny diffusion leading to an inconvenient steady increase of the kinetic energy. We propose the stochastic Schrödinger--Newton equation which contains the above two gravity-related modifications together. Then the wave functions of free macroscopic bodies will gradually and stochastically collapse to solitons which perform inertial motion without the momentum diffusion: conservation of momentum and energy is restored.
arXiv comment7pp
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