Levinson theorem for Dirac particles in two dimensions

1998/05/01 by Qiong-gui Lin, Qiong-Gui Lin
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Topological Materials and Phenomena #quant-ph

paper · pdf · doi:10.1103/physreva.57.3478

published as Phys.Rev. A57 (1998) 3478-3488 · LaTeX, no figure

openalex publication_date 1998/05/01 · arxiv created 1998/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

The Levinson theorem for nonrelativistic quantum mechanics in two spatial dimensions is generalized to Dirac particles moving in a central field. The theorem relates the total number of bound states with angular momentum j (j=\ifmmode±\else\textpm\fi(1)/(2),\ifmmode±\else\textpm\fi(3)/(2),…), n_j, to the phase shifts \ensuremathη_j(\ifmmode±\else\textpm\fiE_k) of scattering states at zero momentum as follows: \ensuremathη_j(\ensuremathμ)+\ensuremathη_j(\ensuremath-\ensuremathμ)=n_j\ensuremathπ.

Citations

• Levinson theorem in two dimensions
• Levinson’s theorem for Dirac particles