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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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The stability of matter: from atoms to stars
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by Elliott H. Lieb PDF
Bull. Amer. Math. Soc. 22 (1990), 1-49
    [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.
  • J. F. G. Auchmuty and Richard Beals, Variational solutions of some nonlinear free boundary problems, Arch. Rational Mech. Anal. 43 (1971), 255–271. MR 337260, DOI 10.1007/BF00250465
  • Encyclopedia of physics, Addison-Wesley Publishing Co., Reading, Mass., 1981. Edited and with a preface by Rita G. Lerner and George L. Trigg; With a foreword by Walter Sullivan. 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.
  • Joseph G. Conlon, The ground state energy of a classical gas, Comm. Math. Phys. 94 (1984), no. 4, 439–458. MR 763746, DOI 10.1007/BF01403881
  • Joseph G. Conlon, Elliott H. Lieb, and Horng-Tzer Yau, The $N^{7/5}$ law for charged bosons, Comm. Math. Phys. 116 (1988), no. 3, 417–448. MR 937769, DOI 10.1007/BF01229202
  • Ingrid Daubechies, An uncertainty principle for fermions with generalized kinetic energy, Comm. Math. Phys. 90 (1983), no. 4, 511–520. MR 719431, DOI 10.1007/BF01216182
  • Ingrid Daubechies and Elliott H. Lieb, One-electron relativistic molecules with Coulomb interaction, Comm. Math. Phys. 90 (1983), no. 4, 497–510. MR 719430, DOI 10.1007/BF01216181
  • [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.
  • Charles L. Fefferman, Stability of matter with magnetic fields, Partial differential equations and their applications (Toronto, ON, 1995) CRM Proc. Lecture Notes, vol. 12, Amer. Math. Soc., Providence, RI, 1997, pp. 119–133. MR 1479241, DOI 10.1090/crmp/012/09
  • [FE] E. Fermi, Un metodo statistico per la determinazione di alcune priorieta del’atomo, Atti Acad. Naz. Lincei, Rend. 6 (1927), 602-607.
  • Encyclopedia of physics, Addison-Wesley Publishing Co., Reading, Mass., 1981. Edited and with a preface by Rita G. Lerner and George L. Trigg; With a foreword by Walter Sullivan. MR 592959
  • Ira W. Herbst, Spectral theory of the operator $(p^{2}+m^{2})^{1/2}-Ze^{2}/r$, Comm. Math. Phys. 53 (1977), no. 3, 285–294. MR 436854
  • Peter Hertel, Heide Narnhofer, and Walter Thirring, Thermodynamic functions for fermions with gravostatic and electrostatic interactions, Comm. Math. Phys. 28 (1972), no. 2, 159–176. MR 1552587, DOI 10.1007/BF01645513
  • P. Hertel and W. Thirring, Free energy of gravitating fermions, Comm. Math. Phys. 24 (1971), no. 1, 22–36. MR 1552579, DOI 10.1007/BF01907031
  • [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.
  • Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
  • H. Kalf, U.-W. Schmincke, J. Walter, and R. Wüst, On the spectral theory of Schrödinger and Dirac operators with strongly singular potentials, Spectral theory and differential equations (Proc. Sympos., Dundee, 1974; dedicated to Konrad Jörgens), Lecture Notes in Math., Vol. 448, Springer, Berlin, 1975, pp. 182–226. MR 0397192
  • [LE] A. Lenard, Lectures on the Coulomb stability problem, Lecture Notes in Physics 20 (1973), 114-135.
  • Elliott H. Lieb, The stability of matter, Rev. Modern Phys. 48 (1976), no. 4, 553–569. MR 0456083, DOI 10.1103/RevModPhys.48.553
  • Elliott H. Lieb, On characteristic exponents in turbulence, Comm. Math. Phys. 92 (1984), no. 4, 473–480. MR 736404, DOI 10.1007/BF01215277
  • Elliott H. Lieb, Thomas-Fermi and related theories of atoms and molecules, Rev. Modern Phys. 53 (1981), no. 4, 603–641. MR 629207, DOI 10.1103/RevModPhys.53.603
  • [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.
  • Elliott H. Lieb, The $N^{5/3}$ law for bosons, Phys. Lett. A 70 (1979), no. 2, 71–73. MR 586690, DOI 10.1016/0375-9601(79)90026-4
  • Elliott H. Lieb and Joel L. Lebowitz, The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei, Advances in Math. 9 (1972), 316–398. MR 339751, DOI 10.1016/0001-8708(72)90023-0
  • [LO] E. H. Lieb and S. Oxford, An improved lower bound on the indirect Coulomb energy, Int. J. Quant. Chem. 19 (1981), 427-439.
  • Elliott H. Lieb and Barry Simon, The Thomas-Fermi theory of atoms, molecules and solids, Advances in Math. 23 (1977), no. 1, 22–116. MR 428944, DOI 10.1016/0001-8708(77)90108-6
  • [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.
  • Elliott H. Lieb and Walter E. Thirring, Gravitational collapse in quantum mechanics with relativistic kinetic energy, Ann. Physics 155 (1984), no. 2, 494–512. MR 753345, DOI 10.1016/0003-4916(84)90010-1
  • Elliott H. Lieb and Horng-Tzer Yau, The stability and instability of relativistic matter, Comm. Math. Phys. 118 (1988), no. 2, 177–213. MR 956165, DOI 10.1007/BF01218577
  • Elliott H. Lieb and Horng-Tzer Yau, The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics, Comm. Math. Phys. 112 (1987), no. 1, 147–174. MR 904142, DOI 10.1007/BF01217684
  • Joachim Messer, Temperature dependent Thomas-Fermi theory, Lecture Notes in Physics, vol. 147, Springer-Verlag, Berlin-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.
  • Walter Thirring, Lehrbuch der mathematischen Physik. 4, Springer-Verlag, Vienna, 1980 (German). Quantenmechanik grosser Systeme. [Quantum mechanics of large systems]. MR 587314, DOI 10.1007/978-3-7091-7054-0
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Additional Information
  • Journal: Bull. Amer. Math. Soc. 22 (1990), 1-49
  • MSC (1985): Primary 81H99, 81M05, 85A15; Secondary 81C99, 82A15
  • DOI:
  • MathSciNet review: 1014510