On the Levinson theorem for Dirac operators

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TR Number

Date

1990-01

Journal Title

Journal ISSN

Volume Title

Publisher

AIP Publishing

Abstract

For 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.

Description

Keywords

dirac equation, number theory, operator theory, bound states

Citation

Klaus, M., "On the Levinson theorem for Dirac operators," J. Math. Phys. 31, 182 (1990); http://dx.doi.org/10.1063/1.528858