薛定谔方程的非标准FDTD实现
Non-standard FDTD implementation of the Schrödinger equation
摘要：
在这项工作中，我们应用科尔的非标准形式的FDTD来解决时间相关的薛定谔方程。推导了考虑电子波函数的非标准FDTD方程，其中电子势可以高于或低于电子能量，除了正弦函数被转换为双曲正弦函数外，非标准项几乎相同，因为当势比电子的能量高时，这个参数是虚的。2也介绍了使用这种方法的完全匹配层。
英文摘要：
In this work, we apply the Cole's non-standard form of the FDTD to solve the time dependent Schrödinger equation. We deduce the equations for the non-standard FDTD considering an electronic wave function in the presence of potentials which can be higher or lower in comparison with the energy of the electron. The non-standard term is found to be almost the same, except for a sine functions which is transformed to a hyperbolic sine function,as the argument is imaginary when the potential has higher energy than the electron. Perfectly Matched Layers using this methodology are also presented.
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