On the optical theorem and non-plane-wave scattering in quantum mechanics

In quantum mechanics, the optical theorem states that the extinction cross section is equal (within a prefactor 4π∕k, in which k is a quantum wave number) to the imaginary part of the forward scattering angular function. This theorem is valid for plane wave scattering. We discuss modifications required for non-plane-wave scattering and establish a generalized expression for the extinction cross section in quantum mechanics. Examples are provided for two kinds of quantum shaped beams, namely, Gaussian and Bessel beams.