Levinson theorem for the Dirac equation in D+1 dimensions -: art. no. 062715

In terms of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation with a spherically symmetric potential in D+1 dimensions is uniformly established as a relation between the total number of bound states and the sum of the phase shifts of the scattering states at E=+/-M with a given angular momentum. The critical case, where the Dirac equation has a half bound state, is analyzed in detail. A half bound state is a zero-momentum solution if its wave function is finite but does not decay fast enough at infinity to be square integrable.