Exponentially Accurate Semiclassical Tunneling Wave Functions in One Dimension
Mathematical Physics
2015-05-18 v1 math.MP
Abstract
We study the time behavior of wave functions involved in tunneling through a smooth potential barrier in one dimension in the semiclassical limit. We determine the leading order component of the wave function that tunnels. It is exponentially small in . For a wide variety of incoming wave packets, the leading order tunneling component is Gaussian for sufficiently small . We prove this for both the large time asymptotics and for moderately large values of the time variable.
Cite
@article{arxiv.1003.3280,
title = {Exponentially Accurate Semiclassical Tunneling Wave Functions in One Dimension},
author = {Vasile Gradinaru and George A. Hagedorn and Alain Joye},
journal= {arXiv preprint arXiv:1003.3280},
year = {2015}
}