  In this paper we further explore and develop the quantum continuum mechanics
(CM) of [Tao \emph{et al}, PRL{\bf 103},086401] with the aim of making it
simpler to use in practice. Our simplifications relate to the non-interacting
part of the CM equations, and primarily refer to practical implementations in
which the groundstate stress tensor is approximated by its Kohn-Sham version.
We use the simplified approach to directly prove the exactness of CM for
one-electron systems via an orthonormal formulation. This proof sheds light on
certain physical considerations contained in the CM theory and their
implication on CM-based approximations. The one-electron proof then motivates
an approximation to the CM (exact under certain conditions) expanded on the
wavefunctions of the Kohn-Sham (KS) equations. Particular attention is paid to
the relationships between transitions from occupied to unoccupied KS orbitals
and their approximations under the CM. We also demonstrate the simplified CM
semi-analytically on an example system.
