Levinson theorem for Dirac particles in one dimension
Qiong-gui Lin
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+( Ek) [η-( Ek)] of scattering states with the same parity at zero momentum as follows: η(μ)+η(-μ)π 2[2η(μ) -2η(-μ)]=nπ. The theorem is verified by several simple examples.
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