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Levinson theorem for Dirac particles in one dimension

Qiong-gui Lin
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Abstract

The scattering of Dirac particles by symmetric potentials in one dimension is studied. A Levinson theorem is established. By this theorem, the number of bound states with even (odd) parity, $n_+$ ($n_-$), is related to the phase shifts $η_+(\pm E_k)$ [$η_-(\pm E_k)$] of scattering states with the same parity at zero momentum as follows: $$η_\pm(μ)+η_\pm(-μ)\pm{π\over 2}[\sin^2η_\pm(μ) -\sin^2η_\pm(-μ)]=n_\pmπ.$$ The theorem is verified by several simple examples.

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Qiong-gui Lin. 1999-12-16. Levinson theorem for Dirac particles in one dimension. https://doi.org/10.1007/s100530050379

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