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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2010

Exponentially Accurate Semiclassical Tunneling Wave Functions in One Dimension

Vasile Gradinaru
  • Fonction : Auteur
George A. Hagedorn
  • Fonction : Auteur
Alain Joye

Résumé

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.

Dates et versions

hal-00464798 , version 1 (18-03-2010)

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