https://doi.org/10.1007/s100530050379
Levinson theorem for Dirac particles in one dimension
China Center of Advanced Science and Technology (World
Laboratory),
P.O. Box 8730, Beijing 100080, P.R. China
and
Department of Physics,
Zhongshan University, Guangzhou 510275, P.R. China
Received:
26
August
1998
Revised:
18
January
1999
Published online: 15 December 1999
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 
[ 
]
of scattering states with the same parity at zero momentum as follows:
![$$\eta_\pm(\mu)+\eta_\pm(-\mu)\pm{\pi\over 2}[\sin^2\eta_\pm(\mu) -\sin^2\eta_\pm(-\mu)]=n_\pm\pi.$$](/articles/epjd/abs/1999/11/d8211/d8211_tex_eq3.png)
The theorem is verified by several simple examples.
PACS: 34.10.+x – General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.) / 03.65.-w – Quantum mechanics / 11.80.-m – Relativistic scattering theory
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999
