In this paper, we investigate the finite-time stability (FTS) and finite-time boundedness (FTB) of quantum systems which are governed by Schrodinger's equation. We first study the FTS and FTS at one target state and propose new results for the mentioned quantum systems in the form of sufficient conditions. Then, we present sufficient conditions for the FTB and FTB at one target state in terms of matrix inequalities. One numerical simulation is presented to illustrate the effectiveness of the obtained theoretical result.