Computer simulation of quantum-mechanical tunneling of a Gaussian wave packet

Brent Perreault, Luiz A. Manzoni, Jose Tadeu Lunardi

Sang Pyo Kim, Kyoung Kon Kim

Yong-Peng Zhang, Sheng-Chang Li

Abstract Tunneling time as an important quantity to characterize tunneling process has not been well defined yet in quantum mechanics. In this paper, we adopt the definition of tunneling time given in [S.-C. Li, New J. Phys. 24, 083033 (2022)] to investigate the time spent by a macroscopic quantum wave packet passing through a Gaussian barrier. We show a general scenario of tunneling times in different energy regimes and find that it has a good agreement with the scenario for a rectangular barrier, which verifies the validity of the above definition of tunneling time for the Gaussian barrier. The influence of both incident energy of wave packet and barrier parameters on tunneling time is discussed thoroughly. The connection between tunneling time and tunneling probability for the Gaussian barrier is established as well. In particular, we use the product of the variances of position and momentum to quantify the deformation of wave packet caused by tunneling process and demonstrate that different behaviors of the variances strongly support our oft-emphasized division of energy regimes.

Helmut Kaiser, S. A. Werner, R. Clothier +2 more

Marcin Ostrowski

Abstract In this paper, we examine whether a quantum computer can efficiently simulate quantum processes such as the tunnel effect. We examine a quantum algorithm that calculates the value of transition and reflection coefficients for the Gaussian wave packet scattered on a rectangular potential. We compare the results obtained in this way with the results of classical simulations and analytical calculations

David J. Coughtrie