Sturmian overlap integrals

Shibuya-Wulfman Integrals and Sturmian Overlap Integrals Evaluated... 

Table 7 The first few overlap integrals m., ., = J d jcy (x) /t(x) between displaced Coulomb Sturmians. The definitions of S, 6 and are the same as in Table 6. The integrals were evaluated by means of equation (124)...

Coulomb Sturmians (CSs) are an exponential-type complete set of basis functions which satisfy a Sturm-Liouville equation [2]. The main objective of the present work is to derive an ADT for the Slater-type orbitals (STOs), which are the fundamental ETO, and thereby for the CSs, which are a linear combination of STOs. The expression for the two-center overlap integral is then worked out for the CSs as an illustration and numerical results and conclusions are presented. 

The matrix elements known, the set (6.2.7) can now be integrated with any of the standard methods for the numerical solution of coupled differential equations (see, e.g., Milne (1970)). In order to be able to interpret the results obtained by the Sturmian method in the physical space of SSE states, we need the overlaps between the Sturmian states (6.2.3) and the SSE states (6.1.24). The result is... 

---