Compact Operators and Particle-Bound-State Scattering: One Channel Case

A method for treating particle-bound-state scattering problems is developed which is based on compact operators. The computations necessary are similar to those of variational methods. Being based on compact operators, the method is not subject to the breakdowns which plague variational methods. The method is applied to triplet $s$-wave electron-hydrogen scattering with excellent results. Hulthén's principle can be examined by our analysis and, for one set of basis functions, justified. A simple criterion is obtained for recognizing when results following from the Hulthén principle will be unreliable and a manner of applying Hulthén's principle indicated which always leads to reliable results.