Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

The stability of matter: from atoms to stars


Author: Elliott H. Lieb
Journal: Bull. Amer. Math. Soc. 22 (1990), 1-49
MSC (1985): Primary 81H99, 81M05, 85A15; Secondary 81C99, 82A15
DOI: https://doi.org/10.1090/S0273-0979-1990-15831-8
MathSciNet review: 1014510
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [AI] E. H. Lieb American Institute of Physics Handbook, McGraw-Hill, New York, 1972 third ed., p. 7-6.
  • [AM] P. Armbruster and G. Münzenberg, Creating superheavy elements, Scientific American 260 (1989), 66-72.
  • [AB] J. Auchmuty and R. Beals, Variational solution of some nonlinear free boundary problems, Arch. Rat. Mech. Anal. 43 (1971), 255-271. See also Models of rotating stars, Astrophys. J. 165 (1971), L79-L82. MR 337260
  • [AB] G. Baym, Neutron stars, in Enclyclopedia of Physics, (R. G. Lerner and G. L. Trigg eds.) Addison-Wesley, London, 1981, pp. 659-660. MR 592959
  • [BM] M. Born, Quantenmechanik der Stossvorgânge, Z. Phys. 38 (1926), 803-827.
  • [CH] S. Chandrasekhar, The maximum mass of ideal white dwarfs, Astrophys. J. S. Chandrasekhar, 74 (1931), 81-82. See also On stars, their evolution and stability, Rev. Mod. Phys. 56(1984), 137-147.
  • [CO] J. Conlon, The ground state energy of a classical gas, Comm. Math. Phys. 94 (1984), 439-458. MR 763746
  • [CLY] J. G. Conlon, E. H. Lieb and H-T. Yau, The N, Comm. Math. Phys. 116 (1988), 417-448. MR 937769
  • [DA] I. Daubechies, An uncertainity principle for fermions with generalized kinetic energy, Comm. Math. Phys. 90 (1983), 511-520. MR 719431
  • [DAL] I. Daubechies and E. H. Lieb, One electron relativistic molecules with Coulomb interactions, Comm. Math. Phys. 90 (1983), 497-510. MR 719430
  • [D] F. J. Dyson, Ground state energy of a finite system of charged particles, J. Math. Phys. 8 (1967), 1538-1545.
  • [DL] F. J. Dyson and A. Lenard, Stability of matter. I and II, J. Math. Phys. 8 (1967), 423-434; ibid 9 (1968), 698-711.
  • [FD] C. Fefferman and R. de la Llave, Relativistic stability of matter. I., Rev. Math. Iberoamericana 2 (1986), 119-215. MR 1479241
  • [FE] E. Fermi, Un metodo statistico per la determinazione di alcune priorieta del'atomo, Atti Acad. Naz. Lincei, Rend. 6 (1927), 602-607.
  • [FR] A. P. French, Atoms, in Encyclopedia of Physics, (R. G. Lerner and G. L. Trigg eds.), Addison-Wesley, London (1981), p. 64. MR 592959
  • [H] I. Herbst, Spectral theory of the operator $(p\sp{2}+m\sp{2})\sp{1/2}-Ze\sp{2}/r$, Comm. Math. Phys. 53 (1977), 285-294. Errata, ibid. 55 (1977), 316. MR 436854
  • [HNT] P. Hertel, H. Narnhofer and W. Thirring, Thermodynamic functions for fermions with gravostatic and electrostatic interactions, Comm. Math. Phys. 28(1972), 159-176. MR 1552587
  • [HT] P. Hertel and W. Thirring, Free energy of gravitating fermions, Comm. Math. Phys. 24(1971), 22-36. MR 1552579
  • [J] J. H. Jeans, The mathematical theory of electricity and magnetism, Cambridge Univ. Press, Cambridge, third edition, 1915, p. 168.
  • [JM] M. Jammer, The conceptual development of quantum mechanics, McGraw Hill, New York, 1966.
  • [K] T. Kato, Perturbation theory for linear operators, Springer-Verlag, Heidelberg, 1966. See Remark 5.12 on p. 307. MR 203473
  • [KS] H. Kalf, U.-W. Schminke, J. Walter and R. Wüst, On the spectral theory of Schrödinger and Dirac operators with strongly singular potentials, Lecture Notes in Math., vol. 448 Springer-Verlag, Berlin and New York, 1974, pp. 182-226. MR 397192
  • [LE] A. Lenard, Lectures on the Coulomb stability problem, Lecture Notes in Physics 20 (1973), 114-135.
  • [LI] E. H. Lieb, Stability of matter, Rev. Mod. Phys. 48 (1976), 553-569. MR 456083
  • [L2] E. H. Lieb, On characteristic exponents in turbulence, Comm. Math. Phys. 92 (1984), 473-480. MR 736404
  • [L3] E. H. Lieb, Thomas-Fermi and related theories of atoms and molecules, Rev. Mod. Phys. 53 (1981), 603-641; errata ibid 54 (1982), 311. MR 629207
  • [L4] E. H. Lieb, Bound on the maximum negative ionization of atoms and molecules, Phys. Rev. 29A (1984), 3018-3028. A summary is in Phys. Rev. Lett. 52 (1984), 315-317.
  • [L5] E. H. Lieb, The N5/3 law for bosons, Phys. Lett. A 70 (1979), 71-73. MR 586690
  • [LL] E. H. Lieb and J. L. Lebowitz, The constitution of matter: existence of thermodynamics for systems composed of electrons and nuclei, Adv. in Math. 9 (1972), 316-398. MR 339751
  • [LO] E. H. Lieb and S. Oxford, An improved lower bound on the indirect Coulomb energy, Int. J. Quant. Chem. 19 (1981), 427-439.
  • [LS] E. H. Lieb and B. Simon, The Thomas-Fermi theory of atoms, molecules and solids, Adv. in Math. 23 (1977), 22-116. MR 428944
  • [LT1 ] E. H. Lieb and W. E. Thirring, Bound for the kinetic energy of fermions which proves the stability of matter, Phys. Rev. Lett. 35 ( 1975), 687-689. Errata ibid. 35(1975), 1116.
  • [LT2] 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 and A. Wightman, eds.), Princeton Univ. Press, Princeton, New Jersey, 1976, pp. 269-330.
  • [LT3] E. H. Lieb and W. E. Thirring, Gravitational collapse in quantum mechanics with relativistic kinetic energy, Ann. of Phys. (NY) 155 (1984), 494-512. MR 753345
  • [LY1] E. H. Lieb and H-T. Yau, The stability and instability of relativistic matter, Comm. Math. Phys. 118(1988), 177-213. A summary is in Many-body stability implies a bound on the fine structure constant, Phys. Rev. Lett. 61 (1988), 1695-1697. MR 956165
  • [LY2] E. H. Lieb and W. E. Thirring, The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics, Comm. Math. Phys. 112 (1987), 147-174. A summary is in A rigorous examination of the Chandrasekhar theory of stellar collapse, Astrophys. J. 323(1987), 140-144. MR 904142
  • [M] J. Messer, Temperature dependent Thomas-Fermi theory, Lectures Notes in Physics no. 147, Springer-Verlag, Berlin and New York, 1981. MR 652484
  • [P] W. Pauli, Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren, Z. Phys. 31 (1925), 765-785.
  • [RB] R. Ruffini and S. Bonazzola, Systems of selfgravitating particles in general relativity and the concept of equation of state, Phys. Rev. 187 (1969), 1767—1783.
  • [SE] E. Schrödinger, Quantisierung als Eigenwertproblem, Ann. Phys. 79 (1926), 361-376. See also ibid. 79 (1926), 489-527; 80 (1926), 437-490; 81 (1926), 109-139.
  • [ST] S. L. Shapiro and S. A. Teukolsky, Black holes, white dwarfs and neutron stars, Wiley, New York, 1983.
  • [T] L. H. Thomas, The calculation of atomic fields, Proc. Cambridge Philos. Soc. 23(1927), 542-548.
  • [TW] W. Thirring, A course in mathematical physics, vol. 4, Springer-Verlag, Berlin and New York, 1983. MR 681697

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 81H99, 81M05, 85A15, 81C99, 82A15

Retrieve articles in all journals with MSC (1985): 81H99, 81M05, 85A15, 81C99, 82A15


Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1990-15831-8

American Mathematical Society