Our subject of interest here is entropic forces, as re-interpreted by Verlinde with reference to gravitation, that is, by appealing to Verlinde's conception of an entropic (statistically emergent) gravity advanced in [Physica A 2018, 511, 139]. In a canonical ensemble framework, we will deal with a non relativistic quantum scenario. In it, we perform a non-relativistic Schrödinger treatment (ST) of gravity as an entropic force and are able to detect new kinds of bounded quantum gravitational states, not previously reported. These new bound states would provide us with a novel energy-source, not taken into account as yet. The present entropic force deviates from the Newton's form only at extremely short distances. We propose, by specializing our results to gravitationally interacting bosons, a model for dark matter generation.
Keywords: dark-matter’s origin; gravitational entropic force; non-relativistic Schrödinger treatment.