Tunneling time from locally periodic potential in space fractional quantum mechanics

Abstract

We calculate the time taken by a wave packet to travel through a classically forbidden locally periodic rectangular potential in space fractional quantum mechanics (SFQM). We obtain the closed-form expression of tunneling time from such a potential by stationary phase method. We show that tunneling time depends upon the width b of the single barrier and separation L between the barriers in the limit $$b \rightarrow \infty $$ and therefore generalized Hartman effect does not exist in SFQM. We observe that in SFQM, the tunneling time for large b in the case of locally periodic potential is smaller than the tunneling from a single barrier of the same width b. It is further shown that with the increase in barrier numbers, the tunneling time reduces in SFQM in the limit of large b.