TY - JOUR
T1 - Nonrelativistic Levinson’s theorem in D dimensions
AU - Dong, Shi Hai
AU - Ma, Zhong Qi
PY - 2002
Y1 - 2002
N2 - The Levinson theorem for the Schrödinger equation with a spherically symmetric potential in D dimensions is uniformly established by the Sturm-Liouville theorem. It is shown that the Levinson theorem for the cases without a half bound state does not depend on the spatial dimension D, namely, the phase-shift [Formula Presented] of the scattering state with angular momentum l at zero momentum is equal to the total number [Formula Presented] of bound states multiplied by [Formula Presented] When a half bound state occurs the Levinson theorem may be modified.
AB - The Levinson theorem for the Schrödinger equation with a spherically symmetric potential in D dimensions is uniformly established by the Sturm-Liouville theorem. It is shown that the Levinson theorem for the cases without a half bound state does not depend on the spatial dimension D, namely, the phase-shift [Formula Presented] of the scattering state with angular momentum l at zero momentum is equal to the total number [Formula Presented] of bound states multiplied by [Formula Presented] When a half bound state occurs the Levinson theorem may be modified.
UR - http://www.scopus.com/inward/record.url?scp=85037181453&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.65.042717
DO - 10.1103/PhysRevA.65.042717
M3 - Artículo
SN - 1050-2947
VL - 65
SP - 6
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 4
ER -