  We present a quantum treatment of the Jeans gravitational instability in the
Newtonian limit of the non-minimal matter-curvature coupling gravity model. By
relying on Wigner functions, allowing for the representation of quantum states
in a classical phase space, we formulate a quantum kinetic treatment of this
problem, generalizing the classical kinetic approach [C. Gomes, Eur. Phys. J. C
80, 633 (2020)]. This allows us to study the interplay between non-minimal
matter-curvature coupling effects, quantum effects, and kinetic
(finite-temperature) effects, on the Jeans criterion. We study in detail
special cases of the model (general relativity, f(R) theories, pure non-minimal
coupling, etc.) and confront the model with the observed stability of Bok
globules.
