Levinson theorem with the nonlocal Aharonov-Bohm effect

Levinson theorem for a charged particle moving in an arbitrary short-range potential and the field of the Aharonov-Bohm magnetic flux is established. The theorem constructs the relation δ_α(0)=n_απ between the phase shift δ_α(k) of scattering state at zero momentum and the total number n_α of bound states for the αth angular-momentum channel, where α=|m+μ₀| is a real number (m=integer, and μ₀=-Φ/Φ₀ with Φ being the magnetic flux and Φ₀=hc/e the fundamental flux quantum). The relation means that the phase shift at the threshold of zero momentum can serve as a counter for the bound states in the general angular-momentum channel.