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Limitations on the principle of stationary phase when it is applied to tunneling analysis

Alex E. Bernardini
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Abstract

Using a recently developed procedure - multiple wave packet decomposition - here we study the phase time formulation for tunneling/reflecting particles colliding with a potential barrier. To partially overcome the analytical difficulties which frequently arise when the stationary phase method is employed for deriving phase (tunneling) time expressions, we present a theoretical exercise involving a symmetrical collision between two identical wave packets and an one-dimensional rectangular potential barrier. Summing the amplitudes of the reflected and transmitted waves - using a method we call multiple peak decomposition - is shown to allow reconstruction of the scattered wave packets in a way which allows the stationary phase principle to be recovered.

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Alex E. Bernardini. 2007-01-02. Limitations on the principle of stationary phase when it is applied to tunneling analysis. https://doi.org/10.1103/physreva.74.062111

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