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arXiv · 1712.08008

Tunneling time in space fractional quantum mechanics

Mohammad Hasan·Bhabani Prasad Mandal
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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.

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Mohammad Hasan, Bhabani Prasad Mandal. 2017-12-20. Tunneling time in space fractional quantum mechanics. https://doi.org/10.1016/j.physleta.2017.12.002

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