Two methods of calculating perturbation effects for the Dirac electron equation are discussed. The two radial functions enter symmetrically in the main contributions to the effects calculated. The first method is related to the method of the Riccati equation for ordinary second-order differential equations but differs from it through the use of the ratio of the two radial functions rather than that of the logarithmic derivative of one of them. The second method has some similarity to Milne's phase amplitude method. The methods described have been helpful in the two preceding papers.

• Received 18 July 1949

DOI:https://doi.org/10.1103/PhysRev.76.1307