  Generalized virial theorem for quantum mechanical nonrelativistic and
relativistic systems with translational and rotational symmetry is derived in
the form of the commutator between the generator of dilations G and the
Hamiltonian H. If the conditions of translational and rotational symmetry
together with the additional conditions of the theorem are satisfied, the
matrix elements of the commutator [G, H] are equal to zero on the subspace of
the Hilbert space. Normalized simultaneous eigenvectors of the particular set
of commuting operators which contains H, J^{2}, J_{z} and additional operators
form an orthonormal basis in this subspace. It is expected that the theorem is
relevant for a large number of quantum mechanical N-particle systems with
translational and rotational symmetry.
