TY - JOUR
T1 - Levinson theorem for the Dirac equation in one dimension
AU - Ma, Zhong Qi
AU - Dong, Shi Hai
AU - Wang, Lu Ya
PY - 2006
Y1 - 2006
N2 - 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: δ± (M) + δ± (-M) = (n± +a) π, 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.
AB - 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: δ± (M) + δ± (-M) = (n± +a) π, 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.
UR - http://www.scopus.com/inward/record.url?scp=33745949135&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.74.012712
DO - 10.1103/PhysRevA.74.012712
M3 - Artículo
SN - 1050-2947
VL - 74
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 1
M1 - 012712
ER -