  One of the few exact results for the description of the time-evolution of an
inhomogeneous, interacting many-particle system is given by the Harmonic
Potential Theorem (HPT). The relevance of this theorem is that it sets a tight
constraint on time-dependent many-body approximations. In this contribution, we
show that the original formulation of the HPT is valid also for the case of
spin-, velocity- and density-dependent interactions. This result is completely
general and relevant, among the rest, for nuclear structure theory both in the
case of ab initio and of more phenomenological approaches. As an example, we
report on a numerical implementation by testing the small-amplitude limit of
the time-dependent Hartree-Fock -- also known as Random Phase Approximation
(RPA) -- for the translational frequencies of a neutron system trapped in a
harmonic potential.
