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The quantum Schrödinger-Newton equation is solved for a self-gravitating Bose gas at zero temperature. It is derived that the density is non-uniform and a central hollow cavity exists. On the other hand, the radial distribution of the particle momentum is uniform. The temperature effect is accounted for via the Schrödinger-Poisson-Boltzmann equation, where low and high temperature solutions are obtained. Via the Schrödinger-Yukawa equation, the analysis is extended to a strong self-interactingdoi:10.5281/zenodo.3816413 fatcat:wtpthryrzbdcrjx3oyb476gkee