Quantum scattering in one dimension

Abstract

A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three dimensions. The present discussion illustrates in a simple way the concept of partial-wave decomposition, phase shift, optical theorem and effective-range expansion.

8 pages

Cited by in corpus (25)

• The transfer matrix: a geometrical perspective
• Integral equations of scattering in one dimension
• Effective Field Theory for Rydberg Polaritons
• Surmounting the sign problem in non-relativistic calculations: a case study with mass-imbalanced fermions
• Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices, and particle-partition entanglement
• Universality in one-dimensional fermions at finite temperature: Density, pressure, compressibility, and contact
• Few-fermion systems in one dimension: Ground- and excited-state energies and contacts
• Three-body repulsive forces among identical bosons in one dimension
• Universality of the energy spectrum for two interacting harmonically trapped ultra-cold atoms in one and two dimensions
• Pairing patterns in one-dimensional spin- and mass-imbalanced Fermi gases
• Anomalous frequency shifts in a one-dimensional trapped Bose gas
• Thermal equation of state of polarized fermions in one dimension via complex chemical potentials
• Universality in a one-dimensional three-body system
• Finite-Range Corrections to the Thermodynamics of the One-Dimensional Bose Gas
• On-shell approximation for the s-wave scattering theory
• Geometrical phase shift in Friedel oscillations
• s-wave scattering and the zero-range limit of the finite square well in arbitrary dimensions
• A model study on a pair of trapped particles interacting with an arbitrary effective range
• Thermodynamics of one-dimensional SU(4) and SU(6) fermions with attractive interactions
• Universal relations for hybridized $s$- and $p$-wave interactions from spin-orbital coupling
• In-medium bound-state formation and inhomogeneous condensation in Fermi gases in a hard-wall box
• Singularities in nearly-uniform 1D condensates due to quantum diffusion
• Effective theory for strongly attractive one-dimensional fermions
• Bose-Bose gases with nonuniversal corrections to the interactions: a droplet phase
• Low-energy atomic scattering: s-wave relation between the interaction potential and the phase shift