Iomin Alexander
Department of Physics, Technion, Haifa 32000, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 1):022103. doi: 10.1103/PhysRevE.80.022103. Epub 2009 Aug 28.
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: partial differential/partial differentialt --> partial differential(alpha)/partial differentialt(alpha). It is shown that for alpha=1/2 the fractional SE is isospectral to a comb model. An analytical expression for the Green's functions of the systems are obtained. The semiclassical limit is discussed.
本文介绍了分数阶微积分在量子过程中的应用。特别地，在分数阶时间薛定谔方程（SE）的框架下考虑量子动力学，该方程与标准SE的不同之处在于分数阶时间导数：∂/∂t → ∂^(α)/∂t^(α)。结果表明，当α = 1/2时，分数阶SE与梳状模型等谱。得到了该系统格林函数的解析表达式。并讨论了半经典极限。
