Work supported by U. S. National Science Foundation Grant MPS 71-03375-A03.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. H. Lieb and W. E. Thirring, Phys. Rev. Lett. 35, 687 (1975). See Phys. Rev. Lett. 35, 1116 (1975) for errata.
M. S. Birman, Mat. Sb. 55(97), 125 (1961); Amer. Math. Soc. Translations Ser. 2, 53, 23 (1966).
J. Schwinger, Proc. Nat. Acad. Sci. 47, 122 (1961).
B. Simon, “Quantum Mechanics for Hamiltonians Defined as Quadratic Forms,” Princeton University Press. 1971.
B. Simon, “On the Number of Bound States of the Two Body Schrödinger Equation — A Review,” in this volume.
A. Martin; Helv. Phys. Acta 45, 140 (1972).
H. Tamura, Proc. Japan Acad. 50, 19 (1974).
V. Glaser, A. Martin, H. Grosse and W. Thirring, “A Family of Optimal Conditions for the Absence of Bound States in a Potential,” in this volume.
S. L. Sobolev, Mat. Sb. 46, 471 (1938), in Russian.
_____, Applications of Functional Analysis in Mathematical Physics, Leningrad (1950), Amer. Math. Soc. Transl. of Monographs, 7 (1963).
G. Talenti, Best Constant in Sobolev’s Inequality, Istituto Matematico, Universitá Degli Studi Di Firenze, preprint (1975).
G. Rosen, SIAM Jour. Appl. Math. 21, 30 (1971).
H. J. Brascamp, E. H. Lieb and J. M. Luttinger, Jour. Funct. Anal. 17, 227 (1974).
C. S. Gardner, J. M. Greene, M. D. Kruskal and R. M. Miura, Commun. Pure and Appl. Math. 27, 97 (1974).
S. A. Moszkowski, Phys. Rev. 89, 474 (1953).
A. E. Green and K. Lee, Phys. Rev. 99, 772 (1955).
V. E. Zakharov and L. D. Fadeev, Funkts. Anal, i Ego Pril. 5, 18(1971). English translation: Funct. Anal, and its Appl. 5, 280 (1971).
H. Epstein, Commun. Math. Phys. 31, 317 (1973).
E. Seiler and B. Simon, “Bounds in the Yukawa Quantum Field Theory,” Princeton preprint (1975).
W. Thirring, T7 Quantenmechanik, Lecture Notes, Institut für Theoretische Physik, University of Vienna.
T. Aubin, C. R. Acad. Sc. Paris 280, 279 (1975). The results are stated here without proof; there appears to be a misprint in the expression for Cr, n.
B. Simon, “Weak Trace Ideals and the Bound States of Schrödinger Operators,” Princeton preprint (1975).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg New York
About this chapter
Cite this chapter
Lieb, E.H., Thirring, W.E. (2005). Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities. In: Thirring, W. (eds) The Stability of Matter: From Atoms to Stars. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27056-6_16
Download citation
DOI: https://doi.org/10.1007/3-540-27056-6_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22212-5
Online ISBN: 978-3-540-27056-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)