Abstract
We show that the moments of order γ of the eigenvalues of the Schrödinger Hamiltonian inn dimensions can be related to moments of order less than or equal to γ-1/2 inn+1 dimensions. This makes it possible to improved the bounds on the sum of the eigenvalues in three dimensions and consequently the Lieb-Thiirng bound on the binding energy of matter.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lieb, E.H., Thirring, W.: Phys. Rev. Lett.35, 687 (1975)
Martin, A.: Helv. Phys. Acta45, 140 (1972);
Tamura, H.: Proc. Japan Acad.50, 19 (1974)
Lieb, E.H., Simon, B.: Adv. Math.23, 22 (1977)
Lieb, E.H.: Bull. Am. Math. Soc.82, 751 (1976), Proceedings of Symposia in Pure Mathematics36, 241 (1980), Commun. Math. Phys.92, 473 (1984); See also: Simon, B.: Functional integration and quantum physics, p. 95. New York: Academic Press 1979
Lieb, E.H., Thirring, W.: Studies in mathematical physics, Liebi, E.H., Simon, B., Wightman, A.S. eds., p. 269. Princeton, NJ: Princeton University Press 1976
Aizenman, M., Lieb, E.H.: Phys. Lett.66A, 427 (1978)
Glaser, V., Grosse, H., Martin, A.: Commun. Math. Phys.59, 197 (1978)
See, for instance: Quigg, C., Rosner, J.L.: Phys. Rep.56, 167 (1979); For a rigorous derivative, see for instance: Clark, C.: Siam Review9, 627 (1967)
Glaser, V., Grosse, H., Martin, A.,, Thirring, W.: [5] p. 169
Blanchard, Ph., Rezende, F., Stubbe, J.: Lett. Math. Phys.14, 215 (1987)
Thirring, W.: Commun. Math. Phys.79, 1 (1981)
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Rights and permissions
About this article
Cite this article
Martin, A. New results on the moments of the eigenvalues of the Schrödinger Hamiltonian and applications. Commun.Math. Phys. 129, 161–168 (1990). https://doi.org/10.1007/BF02096784
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02096784