Distributed basis functions: II. A sum rule and further discussion

Karabulut H.

JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS, vol.38, no.14, pp.2427-2442, 2005 (SCI-Expanded) identifier identifier


In a recent paper (Karabulut 2004 J. Phys. B: At. Mol. Opt. Phys. 37 3103), the author presented a formalism to evaluate performance of a distributed basis to span a given function. The key concept in the formalism is the representation power r (k, d) which is an effective measure of the completeness. In this paper a numerical application of this formalism to estimate the magnitude of the error in a variational problem is presented. The analysis in this application also allows us to discuss what happens in the limit of infinitely dense basis functions. A sum rule that the r(k, d) satisfies is derived. The sum rule explains the strange peaks and dips observed in some r (k, d) versus k curves given in that publication.