We present an algorithm for solving the time-dependent Schrödinger equation that is based on the finite-difference expression of the kinetic energy operator. Students who have some knowledge of linear algebra can understand the theory used to derive the algorithm. This is because the finite-difference kinetic energy matrix and the Hückel matrix for linear conjugated hydrocarbons have similar forms. We offer 3 modules that can be used to solve 1-dimensional time-dependent Schrödinger equations, in real time. Module 1 contains two worksheets designed to show quantum dynamics in bound potentials. Module 2 contains 2 worksheets designed to illustrate tunneling. Module 3 contains 2 worksheets set up to illustrate the effect of time-dependent external fields. Further, modules 1 and 3 also include the Verlet algorithm so students can compare the quantum dynamical evolution of the systems to their classical counterpart in real time.

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实时观察量子动力学：解决时间相关的Schrödinger方程的Excel就绪型有限差分算法

我们提出了一种基于动能算子的有限差分表达式来求解与时间相关的薛定ding方程的算法。掌握线性代数知识的学生可以理解用于推导该算法的理论。这是因为线性共轭烃的有限差分动能矩阵和Hückel矩阵具有相似的形式。我们提供3个模块，可用于实时求解一维时间相关的Schrödinger方程。模块1包含两个工作表，旨在显示束缚势中的量子动力学。模块2包含2个工作表，旨在说明隧道。模块3包含2个工作表，用于说明时间相关的外部字段的影响。进一步，