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arXiv quant-ph/0411113quant-ph
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动电位阶跃下的反射和透射分析

Analyses of reflection and transmission at moving potential step

Toshiharu Samura, Masato Ohmukai

备注：
9 pages, 2 figures
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摘要：

波函数在势阶上的反射和透射是量子力学教科书中的一个著名问题。通过求解含时的薛定谔方程，解析地研究了位阶以与入射波函数同向的恒定速度$v$运动时的反射和透射特性.对于无限大的势阶，群速度等于势阶的运动速度。当势阶具有有限高度$V_0$时，我们发现了两个有趣的结果。当入射波函数的动能大于$(\sqrt{\frac{m}{2}}v + \sqrt{V_0})^2$的有效位高时，发生透射。另一个结果是，反射率取决于$x$，它来自于入射和反射波函数之间的干涉。

英文摘要：

The reflection and transmission of wave functions at a potential step is a well-known issue in a textbook of quantum mechanics. We studied the reflection and transmission characteristics analytically when the potential step is moving at a constant velocity $v$ in the same direction as an incident wave function by means of solving the time-dependent Schrödinger equation. As for an infinite potential step, it is known that group velocity is the same as the moving velocity of the potential step. We found two interesting results when the potential step has a finite height of $V_0$. The transmission occurs when the kinetic energy of incident wave function is larger than the effective potential hight of $(\sqrt{\frac{m}{2}}v + \sqrt{V_0})^2$. The other result is that the reflectivity depends on $x$, which derives from the interference between the incident and the reflected wave functions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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