【摘要】 基于分裂算符法对一维Gross-Pitaevskii方程进行了数值求解，将进出势垒时波函数模方的最大值对应的时刻差值定义为量子隧穿时间，得到了其亮孤子解在不同能量下通过一个确定宽度的高斯型势垒的隧穿时间以及隧穿概率.研究发现，在入射波包能量小于势垒高度时，隧穿时间随入射能量的增大而增大；入射波包能量大于势垒高度时，隧穿时间与波包速度成反比.此外，我们还研究了在不同能量范围内，势垒做小幅度振动时，振动频率对量子隧穿时间以及隧穿概率的影响，观察到了在入射波包能量小于势垒高度的量子状态下，势垒振动频率的不同引起了隧穿时间较大幅度的震荡.更多还原

【Abstract】 We utilized the split-operator method to numerically solve the one-dimensional Gross-Pitaevskii equation. The quantum tunneling time was defined as the time difference corresponding to the maximum value of the modulus square of the wave function when entering and exiting the barrier. We obtain the tunneling time and tunneling probability of its bright soliton solution through a Gaussian potential barrier of a certain width at different energies. It was observed that when the incident energy is less than the barrier height, the tunneling time increases with the incident energy. When the incident energy is greater than the barrier height, the tunneling time is inversely proportional to the tunneling velocity. Furthermore, within different energy ranges, the effects of the oscillation frequency of the barrier on the quantum tunneling time and probability were studied when the barrier undergoes small-amplitude oscillations. It is observed that under the quantum state with incident energy less than the barrier height, different barrier oscillation frequencies caused significant oscillations in the tunneling time.更多还原