Abstract
The H- ion, made up of a proton and two electrons, has long been known to have at least one bound state below the lowest breakup threshold. Variational calculations of sufficient accuracy to demonstrate this appeared shortly after the discovery of the Schrodinger equation. A rigorous demonstration that additional bound states do not exist below the lowest breakup threshold first appeared in 1977.1,2 The present paper will review that proof, prove the new result that the three electron system H- has no bound states below the continuum in the spin 3/2 sector, and discuss related unsolved problems.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
R. N. Hill, Phys. Rev. Lett. 38, 643–646 (1977).
R. N. Hill, J. Math. Phys. 18, 2316 (1977).
The method used here generalizes a method introduced in N. W. Bailey, Proc. Natl. Acad. Sci. U. S. A. 45, 850–853 (1959) and Phys. Rev. 120,.144–149 (1960).
G. W. F. Drake, Phys. Rev. Lett. 24, 126–127 (1970).
I. Aronson, C. J. Kleiman, and L. Spruch, Phys. Rev. A 4, 841–846 (1971).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1980 Springer-Verlag
About this paper
Cite this paper
Hill, R.N. (1980). Proff that the H- ion has only one bound state: A review, a new result, and some related unsolved problems. In: Osterwalder, K. (eds) Mathematical Problems in Theoretical Physics. Lecture Notes in Physics, vol 116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09964-6_300
Download citation
DOI: https://doi.org/10.1007/3-540-09964-6_300
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09964-2
Online ISBN: 978-3-540-39174-6
eBook Packages: Springer Book Archive