  The physical relevance of the fractional time derivative in quantum mechanics
is discussed. It is shown that the introduction of the fractional time
Scr\"odinger equation (FTSE) in quantum mechanics by analogy with the
fractional diffusion $\frac{\prt}{\prt t}\rightarrow \frac{\prt^{\alpha}}{\prt
t^{\alpha}}$ can lead to an essential deficiency in the quantum mechanical
description, and needs special care. To shed light on this situation, a quantum
comb model is introduced. It is shown that for $\alpha=1/2$, the FTSE is a
particular case of the quantum comb model. This \textit{exact} example shows
that the FTSE is insufficient to describe a quantum process, and the appearance
of the fractional time derivative by a simple change $\frac{\prt}{\prt
t}\rightarrow \frac{\prt^{\alpha}}{\prt t^{\alpha}}$ in the Schr\"odinger
equation leads to the loss of most of the information about quantum dynamics.
