传递矩阵法求解有效质量薛定谔方程的精度
Accuracy of transfer matrix approaches for solving the effective mass Schrödinger equation
摘要：
本文用解析法和数值法研究了在求解任意一维势流的定态有效质量薛定谔方程时，不同的传递矩阵方法的精度。被认为是一个常数和位置相关的有效质量的情况下。与有限差分法的比较也进行了。基于分析模型的潜力，以及自洽薛定谔-泊松模拟的异质结器件，它表明，对称化的传输矩阵的方法产生类似的精度作为艾里函数方法在显着降低数值成本，而且避免了与艾里函数的数值问题。
英文摘要：
The accuracy of different transfer matrix approaches, widely used to solve the stationary effective mass Schrödinger equation for arbitrary one-dimensional potentials, is investigated analytically and numerically. Both the case of a constant and a position dependent effective mass are considered. Comparisons with a finite difference method are also performed. Based on analytical model potentials as well as self-consistent Schrödinger-Poisson simulations of a heterostructure device, it is shown that a symmetrized transfer matrix approach yields a similar accuracy as the Airy function method at a significantly reduced numerical cost, moreover avoiding the numerical problems associated with Airy functions.
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