An introductory essay—the development of QDT

In this chapter, the author considers some problems relating to the structure and origins of quantum defect theory (QDT). The Coulomb functions are, of course, special cases of confluent hyper-geometric functions and one might have thought that they had been studied in exhaustive detail by applied mathematicians. However, a number of properties important for QDT had not been stated clearly. The author considers effective range theory to be the more general term and QDT to be a special case for which the outer-region potential has an attractive Coulomb form. A special feature of the attractive Coulomb potential is that it gives an infinite Rydberg series of bound states, and infinite series of resonances converging to each new threshold. There are two types of users of QDT: those who employ the formulae for empirical fitting of data from experiments or computations, and those who obtain all quantities in the formulae from ab initio calculations.