物理与工程

势垒隧穿是初等量子力学中的一个重要模型，但由于求解其波函数涉及超越方程，因此在许多初等量子力学教材中往往着重对透射系数的讲解，很少提及其波函数演化，在部分教材中虽有提及，但往往采用图解法，不利于初学者对该过程的理解。本文针对这一问题，提出了一种便于初学者理解的数值计算方法。该方法根据矩阵力学的向量化思想，将薛定谔方程中的波函数与算符分别以向量和矩阵的形式进行离散化，并利用Julia编程对几种势垒情况下的波函数隧穿的含时演化进行数值模拟。

Quantum tunneling is an important model in elementary quantum mechanics. However, since solution of its wave function involves transcendental equation, many elementary quantum mechanics textbooks often focus on the explanation of transmission coefficient, and rarely mention the evolution of wave function. Although this process is mentioned in some textbooks, it is often solved by graphic method, which is not conducive to beginners' understanding of the process. In this paper, a numerical calculation method for beginners is proposed to solve this problem. According to Dirac's vectorization idea, the state vectors and operators in the Schrodinger equation are discretized in the form of vectors and matrices, respectively, and the time-dependent evolution of wave function tunneling under several potential barriers is solved by Julia numerically.