Numerical Solution of Quantum-Mechanical Pair Equations

Abstract

We discuss and illustrate the numerical solution of the differential equation satisfied by the first‐order pair functions of Sinanoğlu. 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 ${\text{1\hspace{0.17em}/\hspace{0.17em}r}}_{12}$ as the perturbation. The results are accurate and encouraging, and since the method is numerical they are indicative of its potential for obtaining atomic‐pair functions in general.