The Dirac theory of radiation gives a satisfactory account of the absorption, emission, and dispersion of radiation by atoms. Beyond this, quantum electrodynamics also provides a satisfactory treatment of interference phenomena. The results of the theory in most cases agree with what is expected from the correspondence principle, but the calculations which lead to this objective have hitherto been rather complicated, and the simplest consequences of classical radiation theory can only be derived along the circuitous route through a quite nontransparent Schrödinger equation in an infinite-dimensional space.

Below we shall describe a method for treating radiation problems which connects, much more closely than the previous ones, the intuitive conceptions of classical theory with those of wave mechanics and which therefore, in most cases, and without detours, yields the result expected in terms of the correspondence principle.

In this method, the starting point shall not be the Hamiltonian function or the corresponding Schrödinger equation in configuration space but rather the equations of motion, i.e. the Maxwell and Dirac wave equations. These differential equations are integrated explicitly, after the value of the wave functions (E, H, and ψσ) at time t = 0 are regarded as given; here it should be noted that the wave functions at time t = 0 are noncommuting quantities. This noncommutability of the initial values of E, H, and ψσ does not disturb the integration, however, as long as the interaction between matter and radiation is assumed to be small and only linear terms in this interaction are considered.