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Kinetic energy bounds and their application to the stability of matter

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References

  1. M. Aizenman and E.H. Lieb, On semiclassical bounds for eigenvalues of Schrödinger operators, Phys. Lett. 66A, 427–429 (1978).

    Google Scholar 

  2. J. Conlon, E.H. Lieb and H.-T. Yau, The N 7/5 law for bosons, Commun. Math. Phys. (submitted).

    Google Scholar 

  3. M. Cwikel, Weak type estimates for singular values and the number of bound states of Schrödinger operators, Ann. Math. 106, 93–100 (1977).

    Google Scholar 

  4. I. Daubechies, Commun. Math. Phys. 90, 511–520 (1983).

    Google Scholar 

  5. F.J. Dyson, Ground state energy of a finite systems of charged particles, J. Math. Phys. 8, 1538–1545 (1967).

    Google Scholar 

  6. E.H. Lieb, The number of bound states of one-body Schrödinger operators and the Weyl problem, A.M.S. Proc. Symp. in Pure Math. 36, 241–251 (1980). The results were announced in Bull. Ann. Math. Soc. 82, 751–753 (1976).

    Google Scholar 

  7. E.H. Lieb, An L p bound for the Riesz and Bessel potentials of orthonormal functions, J. Funct. Anal. 51, 159–165 (1983).

    Google Scholar 

  8. E.H. Lieb, On characteristic exponents in turbulence, Commun. Math. Phys. 92, 473–480 (1984).

    Google Scholar 

  9. E.H. Lieb and M. Loss, Stability of Coulomb systems with magnetic fields: II. The many-electron atom and the one-electron molecule, Commun. Math. Phys. 104, 271–282 (1986).

    Google Scholar 

  10. E.H. Lieb and W.E. Thirring, Bounds for the kinetic energy of fermions which proves the stability of matter, Phys. Rev. Lett. 35, 687–689 (1975). Errata 35, 1116 (1975).

    Google Scholar 

  11. E.H. Lieb and W.E. Thirring, “Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities” in Studies in Mathematical Physics (E. Lieb, B. Simon, A. Wightman eds.) Princeton University Press, 1976, pp. 269–304.

    Google Scholar 

  12. E.H. Lieb and W.E. Thirring, Gravitational collapse in quantum mechanics with relativistic kinetic energy, Ann. of Phys. (NY) 155, 494–512 (1984).

    Google Scholar 

  13. E.H. Lieb and H.-T. Yau, The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics, Commun. Math. Phys. 112, 147–174 (1987).

    Google Scholar 

  14. G.V. Rosenbljum, Distribution of the discrete spectrum of singular differential operators. Dokl. Akad. Nauk SSSR 202, 1012–1015 (1972). (MR 45 #4216). The details are given in Izv. Vyss. Ucebn. Zaved. Matem. 164, 75–86 (1976). (English trans. Sov. Math. (Iz VUZ) 20, 63–71 (1976).)

    Google Scholar 

  15. E.H. Lieb and H.T. Yau, The stability and instability of relativistic matter, Commun. Math. Phys. 118, 177–213 (1988). For a short summary see: Many body stability implies a bound on the fine structure constant, Phys. Rev. Lett. 61, 1695–1697 (1988).

    Google Scholar 

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Helge Holden Arne Jensen

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© 1989 Springer-Verlag

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Lieb, E.H. (1989). Kinetic energy bounds and their application to the stability of matter. In: Holden, H., Jensen, A. (eds) Schrödinger Operators. Lecture Notes in Physics, vol 345. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51783-9_24

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  • DOI: https://doi.org/10.1007/3-540-51783-9_24

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  • Print ISBN: 978-3-540-51783-2

  • Online ISBN: 978-3-540-46807-3

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