Levinson's Theorem for Dirac Equation

Details Levinson's Theorem for Dirac Equation Levinson's Theorem for Dirac Equation

1993-02-19

arxiv.org/abs/hep-th/9302093v3

Phys.Rev.Lett. 70 (1993) 2507-2510

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, Preprint WIS-92/101/DEC-PH, REVTEX-file (the final argument in the proof of the theorem is given in more detail)

Scientific paper

10.1103/PhysRevLett.70.2507

Levinson's theorem for the Dirac equation is known in the form of a sum of positive and negative energy phase shifts at zero momentum related to the total number of bound states. In this letter we prove a stronger version of Levinson's theorem valid for positive and negative energy phase shifts separately. The surprising result is, that in general the phase shifts for each sign of the energy do not give the number of bound states with the same sign of the energy (in units of $\pi$), but instead, are related to the number of bound states of a certain Schr\"odinger equation, which coincides with the Dirac equation at zero momentum.

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