Abstract
From the equations of general relativity for the radius of a closed homogeneous isotropic universe a Schrödinger equation for a particle is obtained. In the case of a universe filled with pressureless matter (dust) the equation is like that for thes states of a hydrogenlike atom. The miniuniverses obtained in this way have quantized masses of the order of the Planck mass.
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References
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Rosen, N. Quantum mechanics of a miniuniverse. Int J Theor Phys 32, 1435–1440 (1993). https://doi.org/10.1007/BF00675204
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DOI: https://doi.org/10.1007/BF00675204