The quantum balance equations are derived for the number of particles, the momentum, the energy, and the magnetic moment density. These equations in the classical limit ħ → 0 transform into the well-known balance equations. The equation for the magnetic moment is a generalization of the Bloch equation. It is also shown that the spin-spin interaction Hamiltonian, conventionally used in the quantum theory of a many-particle system, yields incorrect equations for the magnetic field in a medium and that this defect can be eliminated. An important role of the Bohm quantum potential is demonstrated for a system of identical bosons and fermions.