Horizon quantum mechanics of collapsing shells

We study the probability that a horizon appears when concentric shells of matter collide, by computing the horizon wave-function of the system. We mostly consider the collision of two ultra-relativistic shells, both shrinking and expanding, at the moment their radii are equal, and find a probability that the system is a black hole which is in qual- itative agreement with what one would expect according to the hoop conjecture and the uncertainty principle of quan- tum physics, and parallels the results obtained for simpler sources. One new feature however emerges, in that this prob- ability shows a modulation with the momenta of the shells and the radius at which the shells collide, as a manifesta- tion of quantum mechanical interference. Finally, we also consider the case of one light shell collapsing into a larger central mass.