Simple Generalization of the Quantum Mechanical Virial Theorem for Nonrelativistic Systems with Rotational Symmetry

In this paper we show that the generalization of the virial theorem can be achieved for nonrelativistic quantum mechanical systems under the conditions of rotational symmetry and the constancy of the trace of moment of inertia tensor. Under these conditions the matrix elements of the commutator of the generator of dilations G and the Hamiltonian H are equal to zero on the subspace of the Hilbert space generated by the simultaneous eigenvectors of the particular maximal set of commuting self-adjoint operators which contains H, J2, Jz, the trace of the moment of inertia tensor TrI and additional operators. The result obtained is relevant for an important class of N-particle nonrelativistic quantum mechanical systems.