Levinson theorem for Aharonov-Bohm scattering in two dimensions

Denis D. Sheka, Franz G. Mertens
2006 Physical Review A. Atomic, Molecular, and Optical Physics  
We apply the recently generalized Levinson theorem for potentials with inverse square singularities [Sheka et al, Phys.Rev.A, v.68, 012707 (2003)] to Aharonov-Bohm systems in two-dimensions. By this theorem, the number of bound states in a given m-th partial wave is related to the phase shift and the magnetic flux. The results are applied to 2D soliton-magnon scattering.
doi:10.1103/physreva.74.052703 fatcat:swrd4q4n7zbjhdsji6qzp5esvq