Optical theorem and Aharonov-Bohm scattering

A rigorous derivation of the optical theorem (OT) from the conservation of probability flux (CPF) is presented for scattering on an arbitrary spherically symmetric potential in N-spatial dimensions (ND). The constructed expression for the OT is found to yield the corresponding well-known results for two- and three-dimensional cases in a rather natural way. The Aharonov-Bohm (AB) effect is considered as a scattering event of an electron by a magnetic field confined in an infinitely long shielded solenoid and a similar derivation is attempted for an appropriate optical theorem. Our current understanding of the scattering theory is found to be inadequate for the purpose. The reason for this is discussed in some detail.