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arXiv · 1003.3280

Exponentially Accurate Semiclassical Tunneling Wave Functions in One Dimension

Vasile Gradinaru·George A. Hagedorn·Alain Joye
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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 $1/\hbar$. 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.

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Vasile Gradinaru, George A. Hagedorn, Alain Joye. 2010-03-17. Exponentially Accurate Semiclassical Tunneling Wave Functions in One Dimension. https://doi.org/10.1088/1751-8113/43/47/474026

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