Levinson's Theorem for the Klein-Gordon Equation in Two Dimensions

Abstract

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 $E=\pm M$.

Revtex file 14 pages, submitted to Phys. Rev. A

References in corpus (7)

• The Relativistic Levinson Theorem in Two Dimensions
• Variable-phase method and Levinson's theorem in two dimensions: Application to a screened Coulomb potential
• Levinson theorem in two dimensions
• Levinson's theorem and scattering phase shift contributions to the partition function of interacting gases in two dimensions
• Levinson theorem for Dirac particles in two dimensions
• Levinson's theorem for the Schrödinger equation in two dimensions
• Levinson's Theorem for Non-local Interactions in Two Dimensions

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