Tunneling time in space fractional quantum mechanics

TL;DR

This paper investigates tunneling times in space fractional quantum mechanics, revealing that tunneling time decreases with barrier width and the Hartman effect is absent, contrasting with standard quantum mechanics.

Contribution

It provides a closed-form expression for tunneling time in space fractional quantum mechanics and shows how it differs from standard quantum mechanics.

Findings

Tunneling time depends on barrier width for large widths.

Tunneling time decreases monotonically with increasing barrier width.

Tunneling time is smaller than in standard quantum mechanics.

Abstract

We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width $b$ of the barrier for $b \to \infty$ and therefore Hartman effect doesn't exist in space fractional quantum mechanics. Interestingly we found that the tunneling time monotonically reduces with increasing $b$. The tunneling time is smaller in space fractional quantum mechanics as compared to the case of standard quantum mechanics. We recover the Hartman effect of standard quantum mechanics as a special case of space fractional quantum mechanics.