Irregular wavefunction behavior in diamagnetic Rydberg hydrogen atoms: a dynamical SO (4, 2) group study

Abstract

We extend the dymanical SO (4, 2) group to the study of the wavefunction behavior of diamagnetic Rydberg hydrogen atoms. The dynamical group allows a complete algebraization of the problem. When coupled with the use of the mini-max theorem, the procedure leads to an efficient algorithm for obtaining accurate eigenvalues and eigenvectors of arbitary highly excited states. Comparison of the classical and quantal behavior in both the regular and irregular regions is presented.