Collisions in low dimensions

Quantum collision theory in three dimensions (3D) has been developed since the early days of quantum mechanics, that is, since the early 20th century. Most of the advancements in three-dimensional low-energy collision physics happened in the 1930s and 1940s, in parallel with the developments in atomic and nuclear physics. Collisions in lower dimensions, that is, in one dimension (1D) and two dimensions (2D), began to attract research interest in the latter half of the 20th century. Early studies of the theory of scattering in 1D appeared in the 1960s. From an experimental point of view, interest in one-dimensional scattering arose from the analysis of tunneling phenomena in a superlattice. Scattering in 2D began to attract attention following experiments involving helium atoms adsorbed on graphite and spin-polarized hydrogen atoms on a helium film. Research interest in bound states in 2D started with theoretical investigations of the problem of hydrogen in 2D and the problem of Coulomb scattering in 2D. These early developments in low-dimensional physics established that the two- and many-body properties of interacting systems in 1D or 2D are qualitatively different from those in 3D.