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Levinson theorem for Dirac particles in two dimensions

Qiong-gui Lin
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Abstract

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=\pm 1/2, \pm 3/2, ... $), $n_j$, to the phase shifts $η_j(\pm E_k)$ of scattering states at zero momentum as follows: $η_j(μ)+η_j(-μ)= n_jπ$.

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Qiong-gui Lin. 1998-06-23. Levinson theorem for Dirac particles in two dimensions. https://doi.org/10.1103/physreva.57.3478

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