On fractional time quantum dynamics

Application of the fractional calculus to quantum processes is presented. In particular, the quantum dynamics is considered in the framework of the fractional time Schr\"odinger equation (SE), which differs from the standard SE by the fractional time derivative: $\frac{\prt}{\prt t}\to \frac{\prt^{\alpha}}{\prt t^{\alpha}}$. It is shown that for $\alpha =1/2$ 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.