Controlling the Aharonov–Bohm Scattering

ABSTRACT This paper proposes a novel approach to controlling the amplitude of the Aharonov–Bohm effect by utilizing a conformal mapping‐based method. The core idea is to leverage the form‐invariance of the Schrödinger equation under conformal transformations, which allows for the manipulation of the scattering amplitude through a carefully designed scalar potential. This approach extends the concept of transformation physics into charge‐flux systems, providing a practical means to steer matter waves influenced by magnetic flux interactions. The paper comprehensively discusses how scalar potentials, determined by conformal mappings, can counterbalance the Aharonov–Bohm scattering, thus offering a new avenue for quantum control by local means rather than purely through non‐local flux interactions.