The Compton Effect in Wave Mechanics

The problem of the scattering of radiation by a free electron has been treated by the author on the basis of Heisenberg's matrix mechanics, which was first modified to be in agreement with the principle of relativity. The main point of this modification is that, whereas in the non-relativity theory one deals with matrices whose elements vary with the time according to the law eiwt, in the relativity theory the elements of the matrices must vary according to the law eiwt′ where t′ = t − (l1x1 + l2x2 + l3x3)/c if they are to determine correctly the radiation emitted in the direction specified by the direction cosines (l1, l2, l3), x1x2 and x3 being the coordinates of the electron at the time t. These matrices were obtained by writing the Hamiltonian equation of the system in the form where W′ is a variable canonically conjugate to t′ and H′ commutes with t′, and then using H′ as an ordinary Hamiltonian function of a dynamical, system that has W′ for its energy and t′ for its time variable.