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中文摘要：
采用量子流体动力学方法（QHD）研究电子穿过隧道结的概率.将复数形式的波函数表示为指数形式,给出Lagrange框架下C和S的时间演化方程,并给出采用时间的二阶差分方法的数值计算过程.由于Lagrange框架下格点随着时间的演化其分布也是变化的,计算过程中涉及到C和S的导数时,直接结合数值计算方法中求函数近似的有理近似方法.以初始波包为高斯波包为例进行了数值计算和分析,所得到的图像明显地显示了量子效应.
英文摘要：
The quantum hydrodynamics dynamics （QHD） is introduced to study the probability of electron through the tunneling junction. The complex form of the wave function was transformed into polar form, the time evolution equations of C and S were given in the Lagrange framework, and the explicit central differencing scheme was adopted for time integration of the QHD equations. In the Lagrangian framework, the grid points of the system will inevitable become scattered and unstructured during the evolution, the spatially smooth functions C and S are especially suitable for rational function approximation method to enable the implementation of a robust numerical scheme. As an example, the dynamics of a Gaussian wave packet is calculated and results are presented in the figures. In these figures, wave packet penetration of the barrier can be clearly observed, showing the quantum effect obviously.
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