分数时间量子动力学
On fractional time quantum dynamics
摘要：
介绍了分数阶微积分在量子过程中的应用。特别地，量子动力学被认为是在分数时间薛定谔方程（SE）的框架下，它不同于标准SE的分数时间导数：$\frac{\prt}{\prt t}\to \frac{\prt^α}{\prt t^α}$。结果表明，对于$α=1/2$，分数阶SE与梳状模型是等谱的.得到了系统格林函数的解析表达式。讨论了半经典极限。
英文摘要：
Application of the fractional calculus to quantum processes is presented. In particular, the quantum dynamics is considered in the framework of the fractional time Schrödinger equation (SE), which differs from the standard SE by the fractional time derivative: $\frac{\prt}{\prt t}\to \frac{\prt^α}{\prt t^α}$. It is shown that for $α=1/2$ the fractional SE is isospectral to a comb model. An analytical expression for the Green functions of the systems are obtained. The semiclassical limit is discussed.
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