利用变分法导出量子力学系统中一类最优控制问题的方程组，并使用具有最优搜索步长的开关变尺度法对最优控制问题进行数值迭代求解，最后在自旋1/2粒子上进行了系统仿真实验，验证了本文方法的有效性，同时对性能指标中参数的不同选择对整个最优控制效果影响的一般规律进行了分析。

Equations set of a class of optimal control problems are deduced in quantum mechanical systems based on variational approach,. Furthermore, an on-off variable metric numerical iterative arithmetic with optimized search step length is used to solve such an optimal problem. Finally, some simulation experiments on a spin-1/2 particle system are done. Experimental results demonstrate the validity of the method proposed. At the same time, the effectiveness of system control under different parameters in the performance index are analyzed.