The nature of dark matter (DM) in modern physics is an important problem. We consider a quantum system consisting of two identical particles which are candidates for the role of DM.We call them graviatoms, and they could be formed in the early Universe. We find the energy spectrum of the gravitatom from DM particles, the Bohr radius, the intensity and frequency of gravitational radiation, and the lifetime of a state. This lifetime is large for superheavy particles. Estimates of these values for different masses of DM particles are given. The amplitude of a gravitational wave from a cloud of dark matter in the Milky Way is also estimated.