Relativistic Levinson theorem in two dimensions

In the light of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation in two dimensions is established as a relation between the total number ni of the bound states and the sum of the phase shifts eta(i)(+/-M) of the scattering states with the angular momentum j: [GRAPHICS] The critical case, where the Dirac equation has a finite zero-momentum solution, is analyzed in detail. A zero-momentum solution is called a half-bound state if its wave function is finite but does not decay fast enough at infinity to be square integrable.