Abstract
A Thomas-Fermi-Weizsäcker type theory is constructed, by means of which we are able to give a relatively simple proof of the stability of relativistic matter. Our procedure has the advantage over previous ones in that the lower bound on the critical value of the fine structure constant, a, is raised from 0.016 to 0.77 (the critical value is known to be less than 2.72). When α = 1/137, the largest nuclear charge is 59 (compared to the known optimum value 87). Apart from this, our method is simple, for it parallels the original Lieb-Thirring proof of stability of nonrelativistic matter, and it adds another perspective on the subject.
This article is dedicated to our colleagues, teachers, and coauthors Klaus Hepp and Walter Hunziker on the occasion of their sexagesimal birthdays. Their enthusiasm for quantum mechanics as an unending source of interesting physics and mathematics has influenced many.
Work partially supported by U.S. National Science Foundation grant PHY95–13072.
Work partially supported by U.S. National Science Foundation grant DMS95–00840.
Work partially supported by European Union, grant ERBFMRXCT960001.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Conlon, J.G., The ground state energy of a classical gas. Commun. Math. Phys. 94, 439–458 (1984).
Daubechies, L, An uncertainty principle for fermions with generalized kinetic energy, Commun. Math. Phys. 90, 511–520 (1983).
Firsov, O.B., Calculation of the interaction potential of atoms for small nuclear separations, Sov. Phys. JETP 5, 1192–1196 (1957).
Hoffmann-Ostenhof, M. and Hoffman-Ostenhof, T., Schrödinger inequalities and asymptotic behavior of the electronic density of atoms and molecules, Phys. Rev. A 16, 1782–1785 (1977).
Kato, T., Remarks on Schrödinger operators with vector potentials. Int. Eq. Operator Theory 1, 103–113 (1978).
Leinfelder, H., Simader, C, Schrödinger operators with singular magnetic vector potentials, Math. Z. 176, 1–19 (1981).
Lieb, E.H. Thomas-Fermi and related theories of atoms and molecules, Rev. Mod. Phys. 53 603–641 (1981). Errata, ibid 54, 311 (1982).
Lieb, E.H., Loss, M. and Solovej, J.P., Stability of Matter in Magnetic Fields, Phys. Rev. Lett. 75, 985–989 (1995).
Lieb, E.H. and Oxford, S., Improved lower bound on the indirect Coulomb energy, Int. J. Quant. Chem. 19, 427–439 (1981).
Lieb, E.H. and Yau, H-T., The stability and instability of relativistic matter, Commun. Math. Phys. 118, 177–213 (1988).
Lieb, E.H., and Thirring, W.E., Bound for the kinetic energy of fermions which proves the stability of matter, Phys. Rev. Lett. 35, 687–689 (1975). Erratum, ibid, 1116.
Rockafellar, R.T., Convex Analysis, Princeton University Press (1970).
Simon, B., Maximal and minimal Schrödinger forms, J. Opt. Theory 1, 37–47 (1979).
Simon, B., Kato’s inequality and the comparison of semigroups, J. Funct. Anal. 32, 97–101 (1979).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lieb, E.H., Loss, M., Siedentop, H. (2001). Stability of Relativistic Matter via Thomas—Fermi Theory. In: Thirring, W. (eds) The Stability of Matter: From Atoms to Stars. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04360-8_35
Download citation
DOI: https://doi.org/10.1007/978-3-662-04360-8_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-04362-2
Online ISBN: 978-3-662-04360-8
eBook Packages: Springer Book Archive