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)].
Categories: quant-ph