  By making use of the Lewis-Riesenfeld invariant theory, the solution of the
Schr\"{o}dinger equation for the time-dependent linear potential corresponding
to the quadratic-form Lewis-Riesenfeld invariant $I_{\rm q}(t)$ is obtained in
the present paper. It is emphasized that in order to obtain the general
solutions of the time-dependent Schr\"{o}dinger equation, one should first find
the complete set of Lewis-Riesenfeld invariants. For the present quantum system
with a time-dependent linear potential, the linear $I_{\rm l}(t)$ and quadratic
$I_{\rm q}(t)$ (where the latter $I_{\rm q}(t)$ cannot be written as the
squared of the former $I_{\rm l}(t)$, {\it i.e.}, the relation $I_{\rm q}(t)=
cI_{\rm l}^{2}(t)$ does not hold true always) will form a complete set of
Lewis-Riesenfeld invariants. It is also shown that the solution obtained by
Bekkar {\it et al.} more recently is the one corresponding to the linear
$I_{\rm l}(t)$, one of the invariants that form the complete set. In addition,
we discuss some related topics regarding the comment [Phys. Rev. A {\bf 68},
016101 (2003)] of Bekkar {\it et al.} on Guedes's work [Phys. Rev. A {\bf 63},
034102 (2001)] and Guedes's corresponding reply [Phys. Rev. A {\bf 68}, 016102
(2003)].
