Summary: The time evolution of a system of coagulating particles is studied within the Marcus-Lushnikov scheme. Each state of the system is characterized by the probability of finding a given set of population numbers of the particles with given mass at time \(t\). The generating functional for these probabilities obeys a Schrödinger-type evolution equation which is solved exactly for the coagulation kernel independent of the masses of colliding particles. I also show that the evolution equation is a good starting point for the asymptotic analysis of its solution in the limit of large total particle numbers.