CCAST, World Lab, Beijing 100080, Peoples R China
; Inst High Energy Phys, Beijing 100039, Peoples R China
; Inst Politecn Nacl, Dept Fis Esc Sup Fis & Matemat, Mexico City 07738, DF, Mexico
The Levinson theorem for the (1+1)-dimensional Dirac equation with a symmetric potential is proved with the Sturm-Liouville theorem. The half-bound states at the energies E=+/- M, whose wave function is finite but does not decay at infinity fast enough to be square integrable, are discussed. The number n(+/-) of bound states is equal to the sum of the phase shifts at the energies E=+/- M:delta(+/-)(M)+delta(+/-)(-M)=(n(+/-)+a)pi, where the subscript +/- denotes the parity and the constant a is equal to -1/2 when no half-bound state occurs, to 0 when one half-bound state occurs at E=M or at E=-M, and to 1/2 when two half-bound states occur at both E=+/- M.