EXPLICIT SUMS AND INTEGRALS OVER COMPLETE-SETS OF INTERMEDIATE STATES OF HYDROGEN

The bound-state and continuum solutions of the Schrödinger equation in a Coulomb potential are presented once again, but in a form that makes similarities in their structure much more apparent than before. The similarity is particularly striking if Laplace transforms are used. Not only are both bound state and continuum solutions of the same form, but they also have a simple structure for arbitrary energy eigenvalues. The usefulness of the formalism is illustrated by considering a number of examples involving infinite sums over bound states and integrals over continuum states of matrix elements that were relevant in past work. © 1995 The American Physical Society.