Levinson theorem for Dirac particles in two dimensions

作者：Qiong-Gui Lin · 发表于：Physical Review A · 年份：1998 · DOI：10.1103/physreva.57.3478 · 被引用次数：22 · 研究领域：Quantum Mechanics and Non-Hermitian Physics、Topological Materials and Phenomena、Quantum chaos and dynamical systems

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 $j$ $(j=\ifmmode\pm\else\textpm\fi{}\frac{1}{2},\ifmmode\pm\else\textpm\fi{}\frac{3}{2},\dots{})$, ${n}_{j},$ to the phase shifts ${\ensuremath{\eta}}_{j}(\ifmmode\pm\else\textpm\fi{}{E}_{k})$ of scattering states at zero momentum as follows: ${\ensuremath{\eta}}_{j}(\ensuremath{\mu})+{\ensuremath{\eta}}_{j}(\ensuremath{-}\ensuremath{\mu}{)=n}_{j}\ensuremath{\pi}$.