Abstract:We apply Milne's phase-amplitude representation [W. E. Milne, Phys. Rev. 35, 863 (1930)] to a scattering problem involving disjoint classically allowed regions separated by a barrier. Specifically, we develop a formalism employing different sets of amplitude and phase functions -each set of solutions optimized for a separate region -and we use these locally adapted solutions to obtain the true value of the scattering phase shift and accurate tunneling rates for ultra-narrow shape resonances. We show results fo… Show more
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