Levinson's theorem for the Klein-Gordon equation in two dimensions

In terms of the modified Sturm-Liouville theorem, the two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential V(r) is established for an angular momentum m as a relation between the numbers n(m)(+/-) of the particle and antiparticle bound states and the phase shifts eta m(+/-M): [GRAPHICS] A solution of the Klein-Gordon equation with the energy M or - M is called a half-bound state if it is finite but does not decay fast enough at infinity to be square integrable. [S1050-2947(99)01702-3].