Abstract: A quantum dynamical algebraic approach is proposed, which is associated with a pair of the raising and lowering opera- tors for solving the bound energy eigen-problem for one-dimensional quantum system with the second Poschl-Teller potential. In addi- tion, the SU（2） Lie algebra related to this quantum system can be built naturally based on the Hamilton operator as well as the raising and lowering operators. The eigen-values and eigen-functions of a physical system in the potential of this kind are also obtained by u- sing the present algebraic technique.

Key words: quantum dynamics, raising and lowering operators, the second Poschl-Teller potential system, SU（2） Lie algebra