Levinson's theorem for the Dirac equation
Abstract
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 π), but instead are related to the number of bound states of a certain Schrödinger equation, which coincides with the Dirac equation at zero momentum.
 Publication:

Physical Review Letters
 Pub Date:
 April 1993
 DOI:
 10.1103/PhysRevLett.70.2507
 arXiv:
 arXiv:hepth/9302093
 Bibcode:
 1993PhRvL..70.2507P
 Keywords:

 03.65.w;
 Quantum mechanics;
 High Energy Physics  Theory;
 Nuclear Theory
 EPrint:
 9 pages, Preprint WIS92/101/DECPH, REVTEXfile (the final argument in the proof of the theorem is given in more detail)