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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 1/1/\hbar. For a wide variety of incoming wave packets, the leading order tunneling component is Gaussian for sufficiently small \hbar. We prove this for both the large time asymptotics and for moderately large values of the time variable.

Keywords

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}
}
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