TY - JOUR
T1 - Levinson theorem for the Dirac equation in [Formula Presented] dimensions
AU - Gu, Xiao Yan
AU - Ma, Zhong Qi
AU - Dong, Shi Hai
PY - 2003
Y1 - 2003
N2 - In terms of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation with a spherically symmetric potential in [Formula Presented] 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 [Formula Presented] 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.
AB - In terms of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation with a spherically symmetric potential in [Formula Presented] 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 [Formula Presented] 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.
UR - http://www.scopus.com/inward/record.url?scp=85037244583&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.67.062715
DO - 10.1103/PhysRevA.67.062715
M3 - Artículo
SN - 1050-2947
VL - 67
SP - 12
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 6
ER -