Regular Article

The dependence of the time delay on the shape of the wave packet tunneling through the potential barrier

Rzhanov Institute of Semiconductor Physics SB RAS 13, Lavrentyev Ave., Novosibirsk 630090, Russia

^a e-mail: bocharov@isp.nsc.ru

Received: 22 January 2020
Received in final form: 12 May 2020
Published online: 4 July 2020

Abstract

The problem of quasi-monochromatic wave packet tunneling through a potential rectangular barrier is studied. It is shown that the approach to calculating the time delay of a wave packet called ``phase time’’ is not universally correct though well known in the literature. In this paper we discuss the mathematical reasons for this discrepancy, and substantiate another, more correct analytical method for calculating the time delay in the approximation of wide barriers. This time depends on the shape of the envelope complex wave function falling on the barrier. Analytical results for the Gaussian wave packet are presented.