TY - JOUR
T1 - Levinson’s theorem for the Schrödinger equation in two dimensions
AU - Dong, Shi Hai
AU - Hou, Xi Wen
AU - Ma, Zhong Qi
PY - 1998
Y1 - 1998
N2 - Levinson’s theorem for the Schrödinger equation with a cylindrically symmetric potential in two dimensions is reestablished by the Sturm-Liouville theorem. The critical case, where the Schrödinger equation has a finite zero-energy solution, is analyzed in detail. It is shown that, in comparison to Levinson’s theorem in the noncritical case, the half bound state for the [Formula Presented] wave, in which the wave function for the zero-energy solution does not decay fast enough at infinity to be square integrable, will cause the phase shift of the [Formula Presented] wave at zero energy to increase an additional [Formula Presented].
AB - Levinson’s theorem for the Schrödinger equation with a cylindrically symmetric potential in two dimensions is reestablished by the Sturm-Liouville theorem. The critical case, where the Schrödinger equation has a finite zero-energy solution, is analyzed in detail. It is shown that, in comparison to Levinson’s theorem in the noncritical case, the half bound state for the [Formula Presented] wave, in which the wave function for the zero-energy solution does not decay fast enough at infinity to be square integrable, will cause the phase shift of the [Formula Presented] wave at zero energy to increase an additional [Formula Presented].
UR - http://www.scopus.com/inward/record.url?scp=0001562091&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.58.2790
DO - 10.1103/PhysRevA.58.2790
M3 - Artículo
SN - 1050-2947
VL - 58
SP - 2790
EP - 2796
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 4
ER -