# 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 $1/\hbar$. 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.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00464798
Contributor : Alain Joye <>
Submitted on : Thursday, March 18, 2010 - 7:11:41 AM
Last modification on : Thursday, January 11, 2018 - 6:12:13 AM

### Identifiers

• HAL Id : hal-00464798, version 1
• ARXIV : 1003.3280

### Citation

Vasile Gradinaru, George Hagedorn, Alain Joye. Exponentially Accurate Semiclassical Tunneling Wave Functions in One Dimension. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2010, 43, pp.474026. ⟨hal-00464798⟩

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