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量子隧道效应的数值计算

Keywords: 量子流体动力学,方势垒,函数近似

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Abstract:

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框架下格点是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的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.

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