Vasile Gradinaru, George A. Hagedorn, Alain Joye
Exponentially Accurate Semiclassical Tunneling Wave Functions in One Dimension
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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.