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The Stability of Matter

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The Schrödinger Equation

Part of the book series: Acta Physica Austriaca ((FEWBODY,volume 17/1977))

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Abstract

An outline is presented of the proofs of three basic facts about quantum-mechanical Coulomb systems: (i) atoms have finite ground state energies; (ii) the energy of bulk matter saturates; (iii) the thermodynamic limit exists.

Work partially supported by U.S. National Science Foundation grant MCS 75-21684.

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References

  1. S.L. Sobolev, Mat. Sb. 46, 471, 1938. See also S.L, Sobolev, Amer. Math. Soc. Trans 1. of Monographs, 7, 1963.

    Google Scholar 

  2. T. Kato, Trans. Amer. Math. Soc. 70, 195, 1951.

    MathSciNet  MATH  Google Scholar 

  3. F.J. Dyson and A. Lenard, J. Math. Phys. 8, 423, 1967. See also A. Lenard and F.J. Dyson, J. Math. Phys. 9, 698, 1968.

    MathSciNet  MATH  Google Scholar 

  4. E.H. Lieb and W.E. Thirring, Phys. Rev. Lett. 35, 687, 1975? Errata: Phys. Rev. Lett, 3J5, 1116, 1975. For more details on kinetic energy inequalities and their application, see also 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: Essays in Honor of Valentine Bargmann, E.H. Lieb, B. Simon and A.S. Wightman editors, Princeton University Press, 1976.

    Google Scholar 

  5. F.J. Dyson, J. Math. Phys. 8, 1538, 1967.

    Article  MathSciNet  ADS  Google Scholar 

  6. E.H. Lieb and B. Simon, Adv. in Math. 1977, in press. See also E.H. Lieb and B. Simon, Phys. Rev. Lett. 33, 681, 1973.

    Google Scholar 

  7. E.H. Lieb and J.L. Lebowitz, Adv. in Math. 9, 316, 19 72. See also J.L. Lebowitz and E.H. Lieb, Phys. Rev. Lett. 22, 631, 1969.

    Google Scholar 

  8. E.H. Lieb, Rev. Mod. Phys. October 1976.

    Google Scholar 

  9. W. Heisenberg, Zeits. Phys. 43, 172, 1927.

    Article  ADS  Google Scholar 

  10. G. Rosen, Siam J. Appl. Math. 21, 30, 1971.

    MATH  Google Scholar 

  11. E.H. Lieb, Bull. Amer. Math. Soc. 1976, in press.

    Google Scholar 

  12. E. Teller, Rev. Mod. Phys. 34, 627, 1962.

    Article  ADS  MATH  Google Scholar 

  13. E.H. Lieb and H. Narnhofer, J. Stat. Phys. 12, 291, 1975. Erratum: J. Stat. Phys. 14, No. 5, 1976.

    Google Scholar 

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© 1977 Springer-Verlag

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Lieb, E.H. (1977). The Stability of Matter. In: Thirring, W., Urban, P. (eds) The Schrödinger Equation. Acta Physica Austriaca, vol 17/1977. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7673-3_9

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  • DOI: https://doi.org/10.1007/978-3-7091-7673-3_9

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-7675-7

  • Online ISBN: 978-3-7091-7673-3

  • eBook Packages: Springer Book Archive

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