%0 Journal Article
%T Levinson's Theorem for the Klein-Gordon Equation in Two Dimensions
%A Shi-Hai Dong
%A Xi-Wen Hou
%A Zhong-Qi Ma
%J Physics
%D 1998
%I arXiv
%R 10.1103/PhysRevA.59.995
%X The two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential $V(r)$ is established. It is shown that $N_{m}\pi=\pi (n_{m}^{+}-n_{m}^{-})= [\delta_{m}(M)+\beta_{1}]-[\delta_{m}(-M)+\beta_{2}]$, where $N_{m}$ denotes the difference between the number of bound states of the particle $n_{m}^{+}$ and the ones of antiparticle $n_{m}^{-}$ with a fixed angular momentum $m$, and the $\delta_{m}$ is named phase shifts. The constants $\beta_{1}$ and $\beta_{2}$ are introduced to symbol the critical cases where the half bound states occur at $E=\pm M$.
%U http://arxiv.org/abs/quant-ph/9808038v1