The problem of the ionized hydrogen molecule
The problem of the ionized hydrogen molecule was first treated by Pauli(1) who used the old quantum theory and obtained a result which was not in agreement with experiment. Niessen,(2) however, obtained the experimental value for the lowest energy level by introducing half-quantum numbers. The problem has now been treated by methods of wave-mechanics; thus Burrau(3) obtained a result in very good agreement with experiment by a numerical integration and a general discussion has been given recently by A. H. Wilson.(4) It is well known that the polynomial method of wave-mechanics, invented by Brillouin and Wentzel and developed by Sommerfeld,(5) gives, for a certain group of problems, the same result as the old quantum theory in approximation (0) and gives half-quantum numbers in approximation (1). It is shown in this paper that the present problem belongs to this group.
© 1929 by the National Academy of Sciences. Communicated May 20, 1929. I am very much indebted to Professor A. Sommerfeld, Professor P.S. Epstein and Professor H. Bateman for the encouragement and suggestions they have given me in the study of this problem. I wish also to express my gratitude to the China Foundation which provides me with a research fellowship.