NUMERICAL SOLUTION OF QUANTUM-MECHANICAL PAIR EQUATIONS

We discuss and illustrate the numerical solution of the differential equation satisfied by the first-order pair functions of Sinanoglu. An expansion of the pair function in spherical harmonics and the use of finite difference methods convert the differential equation into a set of simultaneous equations. Large systems of such equations can be solved economically. The method is simple and straightforward, and we have applied it to the first-order pair function for helium with 1/ris as the perturbation. The results are accurate and encouraging, and since the method is numerical they are indicative of its potential for obtaining atomicpair functions in general.