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We modify the time dependent Schr\"odinger-Newton equation by using apotential for a solid sphere suggested by J\"a\"askel\"ainen(J\"a\"askel\"ainen 2012 Phys. Rev. A 86 052105) as well as a hollow-spherepotential. Compared to our recent paper (Giulini and Gro{\ss}ardt 2011 Class.Quantum Grav. 28 195026) where a single point-particle, i.e. a Coulombpotential, was considered this has been suggested to be a more realistic modelfor a molecule. Surprisingly, compared to our previous results, inhibitions ofdispersion of a Gaussian wave packet occur at even smaller masses for thesolid-sphere potential, given that the width of the wave packet is not exceededby the radius of the sphere.

Gravitationally induced inhibitions of dispersion according to a modified Schr\"odinger-Newton equation for a homogeneous-sphere potential