Limitations of the method of complex basis functions

The method of complex basis functions proposed by Rescigno and Reinhardt is applied to the calculation of the amplitude in a model problem which can be treated analytically. It is found for an important class of potentials, including some of infinite range and also the square well, that the method does not provide a converging sequence of approximations. However, in some cases, approximations of relatively low order might be close to the correct result. The method is also applied to $S$-wave $e$-H elastic scattering above the ionization threshold, and spurious "convergence" to the wrong result is found. A procedure which might overcome the difficulties of the method is proposed.