Scattering resonances and background associated with an asymmetric potential barrier via Siegert pseudostates

The transmission of a nonsymmetric potential barrier is a two-channel quantum problem. In this aspect it is analogous to the two-channel radial problem. The analytical properties of the S matrix are similar for both generic quantum-mechanical systems. We here develop an explicit mapping between the two problems. It allows us to formulate barrier transmission in terms of the Siegert pseudostates similarly to the approach developed recently for the two-channel radial case. This results in an efficient method of treating barrier transmission including on equal footing both resonance effects and smooth background behavior.