Levinson theorem for Dirac particles in one dimension

Details Levinson theorem for Dirac particles in one dimension Levinson theorem for Dirac particles in one dimension

1999-12-16

arxiv.org/abs/quant-ph/9912078v1

Eur. Phys. J. D 7 (1999) 515-524

Physics

Quantum Physics

REVTeX, 17 pages, no figure

Scientific paper

10.1007/s100530050379

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 $\eta_+(\pm E_k)$ [$\eta_-(\pm E_k)$] of scattering states with the same parity at zero momentum as follows: $$\eta_\pm(\mu)+\eta_\pm(-\mu)\pm{\pi\over 2}[\sin^2\eta_\pm(\mu) -\sin^2\eta_\pm(-\mu)]=n_\pm\pi.$$ The theorem is verified by several simple examples.

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