Optical Theorem

In physics, the optical theorem is a general law of wave scattering theory relating the scattering amplitude measured at zero angle to the total cross section of the object doing the scattering. First derived independently by Wolfgang Sellmeier and Lord Rayleigh in 1871 and later extended into quantum scattering theory, where it became known after a 1939 paper as the Bohr-Peierls-Placzek relation, the theorem follows from nothing more than conservation of energy, or in quantum mechanics conservation of probability, which is what makes it apply so broadly across both elastic and inelastic scattering. Werner Heisenberg derived a generalized form of the theorem from the unitarity of the scattering process; the name optical theorem itself first appeared in print in 1955, in a paper by Hans Bethe and Frederic de Hoffmann.