The propagation of boson particles in a gravitational field described by the Brans–Dicke (BD) theory of gravity is analyzed. We derive the wave function of the scalar particles, and the effective potential experienced by the quantum particles considering the role of the varying gravitational coupling. Besides, we calculate the probability to find the scalar particles near the region where a naked singularity is present. The extremely high energy radiated in such a situation could account for the huge emitted power observed in gamma ray bursts (GRBs).