Exponentially Accurate Semiclassical Tunneling Wave Functions in One Dimension

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

References in corpus (4)

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Cited by in corpus (4)

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