The incident wave in Aharonov-Bohm scattering wavefunction

TL;DR

The paper demonstrates that in Aharonov-Bohm scattering, only infinite angular momentum states contribute to the incident wave, clarified through a recalculation with arbitrary decomposition of angular momentum sums.

Contribution

It reveals that the incident wave in AB scattering originates solely from infinite angular momentum quantum states, clarifying the role of pole contributions.

Findings

Incident wave arises only from infinite angular momentum states.

Recalculation confirms the pole contribution corresponds to infinite angular momentum.

Clarifies the mathematical origin of the incident wave in AB scattering.

Abstract

It is shown that only the infinite angular momentum quantum states contribute to the incident wave in Aharonov-Bohm (AB) scattering. This result is clearly shown by recalculating the AB calculation with arbitrary decomposition of summation over the angular momentum quantum numbers in wave function. It is motivated from the fact that the pole contribution in the integral representation used by Jackiw is given by only the infinite angular momentum states, in which the closed contour integration involving this pole gives just the incident wave.