This paper is based on the idea that wave mechanics is primarily suitable for giving an indirect description of nature. The world to which the equations of the theory here proposed are directly applicable is an unnatural one, containing sources and sinks of matter which give to its radiational laws a symmetry lacking in nature. The theory may be regarded as consisting of two postulates. The first (which may, if desired, be regarded as a definition) specifies the character and properties of an unnatural assembly of systems, each consisting of an electron in a static potential field U. It states that, of the energy radiated in an elementary solid angle of standard magnitude, the part which will pass through an analyzer which transmits the component of electric field in a given direction (perpendicular to the line of observation) is determined by applying the usual Schrodinger interpretations (of density, current and material energy) to a Schrodinger equation perturbed by a term which is a certain constant multiplied by the electric field, in that direction, acting on the electron, due to the potential field U. (For comparison with classical radiation theory, it will be noted that the perturbation term vanishes in any region in which, from the classical standpoint, the electron is not accelerated, in that direction, by the field U.) In the process of specifying the radiation from the assembly, the Schrodinger interpretations will have specified also the nature and magnitude of the sources and sinks of electrons (each in a field U). Their presence is due, mathematically speaking, to the multiplying constant mentioned above being a complex quantity. From these results the properties of a natural assembly are specified by means of the second postulate, which states that when the sources and sinks are removed, any process which in their absence is meaningless or physically inconceivable will cease, and all other processes will remain unaffected. The calculation is readily extended to include the effect of an external field of radiation. The theory requires no representation of radiation other than the Maxwellian wave, and will be free from the difficulties encountered in other theories.