Virginia TechKlaus, Martin2014-04-092014-04-091990-01Klaus, M., "On the Levinson theorem for Dirac operators," J. Math. Phys. 31, 182 (1990); http://dx.doi.org/10.1063/1.5288580022-2488http://hdl.handle.net/10919/47071For the Dirac equation with potential V(r) obeying ∫∞ 0(1+r)‖V(r)‖d r<∞ we prove a relativistic version of Levinson’s theorem that relates the number of bound states in the spectral gap [−m,m] to the variation of an appropriate phase along the continuous part of the spectrum. In the process, the asymptotic properties of the Jost function as E→±m are analyzed in detail. The connection with the nonrelativistic version of Levinson’s theorem is also established.application/pdfenIn Copyrightdirac equationnumber theoryoperator theorybound statesArticle - Refereedhttp://scitation.aip.org/content/aip/journal/jmp/31/1/10.1063/1.528858https://doi.org/10.1063/1.528858