Volterra inverse scattering series method for one‐dimensional quantum barrier scattering. Issue 17 (19th May 2017)

• Record Type: Journal Article
• Authors: Chou, Chia‐Chun; Yao, Jie; Kouri, Donald J.
• Is Part Of: International journal of quantum chemistry. Volume 117:Issue 17(2017)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2017-05-19
• Subjects: Green's function -- Lippmann–Schwinger equation -- quantum inverse scattering -- Volterra integral equation; Quantum chemistry -- Periodicals; 541.28
• DOI: 10.1002/qua.25403
• Languages: English
• ISSNs: 0020-7608

Abstract

Abstract: The Volterra inverse scattering series method is developed to obtain the interaction potential for one‐dimensional quantum barrier scattering problems. The Lippmann–Schwinger equation describing quantum barrier scattering is renormalized from a Fredholm to a Volterra integral equation. Employing the Born–Neumann series solution of the Lippmann–Schwinger Volterra equation and a related expansion of the interaction potential in orders of the data, we derive the Volterra inverse scattering series for the reflection and transmission amplitudes. Each term of the interaction potential is computed using the scattering amplitude and the Volterra Green's function. We do not consider the separate issue of extracting scattering amplitudes from quantum cross sections. The triangular nature of the Volterra Green's function significantly reduces computational effort. The Volterra series is then applied to several one‐dimensional quantum barrier scattering problems. Computational results show that the first few terms in the Volterra series can yield accurate interaction barriers. In addition, the potential barriers are calculated using the Born inverse scattering series based on the Lippmann–Schwinger Fredholm equation with the reflection amplitude. The comparison between the Born and Volterra results demonstrates that the Volterra inverse scattering series can provide a more accurate and more efficient method for determining the interaction potential. Abstract : The Volterra inverse scattering series method is developed to obtain the interaction potential for quantum barrier scattering problems. The Lippmann–Schwinger equation is renormalized from a Fredholm to a Volterra integral equation. The Volterra inverse scattering series is derived for the reflection and transmission amplitudes. Each term of the interaction potential is computed using the scattering amplitude and the Volterra Green's function. Computational results indicate that the Volterra series can significantly reduce computational effort.