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

Abstract

Using a recently developed procedure---multiple wave packet decomposition---here we study the phase time formulation for tunneling or 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.