One-Dimensional Scattering

Charles G. Wohl

Lü Xiao

One dimensional and two dimensional Lippmann Schwinger equation and its applications are discussed in quantum scattering.Refection and transmission coefficients of one dimensional scattering and cross sections of two dimensional scattering are given.

Tapan Kumar Das

Chia‐Chun Chou, Róbert E. Wyatt

One-dimensional scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. First, the pole structure of the quantum momentum function for scattering wave functions is analyzed. The significant differences of the pole structure of this function between scattering wave functions and bound state wave functions are pointed out. An accurate computational method for the quantum Hamilton-Jacobi equation for general one-dimensional scattering problems is presented to obtain the scattering wave function and the reflection and transmission coefficients. The computational approach is demonstrated by analysis of scattering from a one-dimensional potential barrier. We not only present an alternative approach to the numerical solution of the wave function and the reflection and transmission coefficients but also provide a computational aspect within the quantum Hamilton-Jacobi formalism. The method proposed here should be useful for general one-dimensional scattering problems.

S. Brandt, Hans Dieter Dahmen

Tomohiro Tanaka, Yusuke Nishida

We investigate two-cluster scattering in a quasi-one-dimensional Bose gas. We focus on the effective three-body interaction induced by transverse confinement, which is the leading term for breaking integrability in the quasi-one-dimensional setting. Exploiting the Lüscher formula and the integrability of the Lieb-Liniger Bose gas, we find a finite and positive scattering length for elastic two-cluster scattering. The resulting scattering lengths indicate the emergence of a resonance.